UNIVERSITY  OF  CALIFORNIA 

MEDICAL  CENTER  LIBRARY 

SAN  FRANCISCO 


^itebfc'K 

^VB 

re* 


*r?^ 


PHYSIOLOGIC  OPTICS 


DIOPTRICS  OF  THE  EYE,  FUNCTIONS  OF  THE  RETINA 
OCULAR  MOVEMENTS  AND  BINOCULAR  VISION 


DR.  M.fTSGHERNING 

ADJUNCT-DIRECTOR.  OF  THE~XABORATORY  OF  OPHTHALMOLOOY 

AT   THE   SORBONNE,    PARIS 


AUTHORIZED  TRANSLATION 

From  the  Original  French  Edition,  Specially  Revised  and  Enlarged  by  the  Author 

BY 

CARL  WEILAND,  M.  D. 

FORMER  CHIEF  OF  CLINIC  IN  THE  EYE  DEPARTMENT  OF  THE   JEFFERSON  MEDICAL   COLLEGB 

HOSPITAL  OF  PHILADELPHIA 


WITH    212    ILLUSTRATIONS 


&P47? 
TS7 


SECOND  EDITION 


PUBLISHED   BY 

THE  KEYSTONE 

E   ORGAN   OF  THE  JEWELRY  AND  OPTICAL,  TRADES 

IQTH  &  BROWN  STS.,  PHILADELPHIA,  U.  S.  A. 
1904 

All  rights  reserved 


171629 


COPYRIGHT,  1900,  BY  B.  THORPE 
PUBLISHER  OF  THE  KEYSTONE 

Entered  at  Stationers'  Hall,  Condon,  Eng. 


TRANSLATOR'S   PREFACE. 


Physiologic  Optics  is  a  science  which,  on  the  one  side,  touches  the 
highest  philosophic  problems  of  the  human  mind  and,  on  the  other  side, 
keeps  in  intimate  contact  with  the  practical  work  of  the  ophthalmologist, 
who,  in  his  daily  work  of  refraction,  can  be  guided  safely  only  by  its 
principles. 

Many  are  the  text-books  on  this  important  subject.  Some  are  mere 
compilations  of  older  facts  and  some  are  written  by  men  that  soar  so  high 
above  the  field  of  the  practical  work  of  the  ophthalmologist  that  their 
abstract  scientific  investigations  lose  almost  all  contact  with  these  practical 
workers. 

The  present  book  is  neither  a  mere  compilation  nor  an  abstract 
theoretical  investigation,  but  a  collection  of  all  the  old  and  new  scientific 
facts  that  have  any  bearing  on  the  practical  work  of  the  oculist  and 
optician.  It  is  written  by  a  man  who  lately  has  probably  done  more 
original  work  in  this  line  than  any  other  since  Helmholtz  and  Bonders, 
and  who,  furthermore,  has  been  in  constant  contact  with  practical  ophthal- 
mology.— Dr.  M.  Tscherning,  who  was  born  in  Denmark  in  1854,  studied 
ophthalmology  at  Copenhagen  under  the  philosophic  mind  of  Hansen  Grut. 
Since  1884  he  has  been  adjunct-director  of  the  laboratory  of  ophthalmology 
at  the  Sorbonne,  where,  since  the  deplorable  disability  of  Javal,  he  himself 
has  performed  the  functions  of  the  director.  This  laboratory,  which  was 
founded  in  1876  for  Javal,  after  he  had  become  widely  known  by  his 
translation  of  the  Physiologic  Optics  of  Helmholtz,  has  given  a  new  impetus 
to  this  science  in  France. 

Here  Tscherning  has  made  all  his  important  original  investigations, 
especially  on  ophthalmometry,  the  catoptric  images  of  the  eye,  astigmatism, 
spherical  aberration  and  accommodation.  All  this  original  work,  as  well 
as  that  of  former  investigators,  is  described  in  this  book  with  great 
clearness  and  succinctness,  almost  entirely  free  from  tedious  mathematical 


encumbrances.  Instead  of  long  formuke,  the  experiment  and  simple 
geometrical  deductions  are  employed  to  explain  the  observed  phenomena. 
The  translator  has  endeavored  to  reproduce  the  clearness  and  brevity  of 
expression  of  the  original  as  much  as  possible.  How  far  he  has  succeeded 
in  this,  it  is  not  for  him  to  judge. 

This  English  edition,  as  has  been  indicated  on  the  title  page,  contains 
many  additions  in  the  text  by  Dr.  Tscherning,  who  has  thus  brought  his 
book  thoroughly  up  to  date.  The  few  notes,  added  by  the  translator,  have 
been  included  in  brackets  with  the  letter  W.  appended.  A  list  of  illustrations 
and  an  index  have  been  compiled  to  enhance  the  practical  value  of  the  book. 

It  is  true  that  some  of  the  ideas  expressed  by  the  author,  especially 
those  about  the  use  of  mydriatics  for  ordinary  purposes  of  refraction 
and  the  use  of  spectacles,  are  not  in  accord  with  current  views  about 
these  subjects  on  this  side  of  the  Atlantic.  But  even  those  who  cannot  agree 
with  the  author  on  these  questions,  will  find  many  new  facts  and  ideas 
which  will  make  a  study  of  the  book  of  great  interest  and  profit.  The 
translator  only  hopes  that  the  reader  may  experience  the  same  intellectual 
pleasure  that  he  felt  while  reading  and  translating  this  work  of  one  of  our 
greatest  investigators  in  the  field  of  physiologic  optics. 

CARL  WEILAND,  M.  D.,  Philadelphia,  U.  S.  A. 


TABLE  OF  CONTENTS 


BOOK  I 

OCULAR  DIOPTRICS 


CHAPTER  I 
OPTIC  PRINCIPLES 

PAGE 

1.  Optic  Properties  of  Bodies I 

2.  Rectilinear  Propagation  of  Light X 

3.  Reflection  and  Absorption 2 

4.  Regular  Reflection 2 

5.  Plane  Mirrors.     Construction  of  the  Image 3 

6.  Concave  Spherical  Mirrors 3 

7.  Convex  Mirrors 6 

8.  Practical  Remarks 6 

9.  Refraction 8 

10.  Quantity  of  Light  Reflected.     Total  Reflection 8 

11.  Refraction  by  Plates  with  Plane  and  Parallel  Surfaces lo 

12.  Refraction  by  a  Prism 10 

13.  Refraction  by  a  Spherical  Surface II 

14.  Infinitely  Thin  Lenses 14 

15.  Theory  of  Gauss 18 

Bibliography 26 


CHAPTER  II 
THE  OPTIC  SYSTEM  OF  THE  EYE 

16.  Optic  Constants  of  the  Eye 27 

17.  Optic  System  of  the  Eye 31 

18.  Aperture  of  the  System 34 

19.  Point  of  Fixation.    Visual  Line 36 

20.  Optic  Axis.    Angle  a 36 

21.  Useful  Image 37 

Bibliography 38 


CHAPTER  III 
THE  FALSE  IMAGES  OF  THE  EYE 

PAGE 

22.  General  Remarks 39 

23.  The  Images  of  Purkinje 40 

24.  Manner  of  Observing  the  Images  of  Purkinje 42 

25.  False  Images  of  the  Second  Order 44 

26.  Manner  of  Observing  the  Sixth  Image 45 

Bibliograpy 46 

CHAPTER  IV 
OPHTHALMOMETRY 

27.  Principles  of  Ophthalmometry 47 

28.  Methods  of  Doubling 48 

29.  The  Ophthalmometer  of  Javal  and  Schiotz 51 

30.  Results  of  the  Measurement  of  the  Cornea 54 

31.  Measurement  of  the  Angle  a       63 

32.  Determination  of  the  Position  of  the  Internal  Surfaces 67 

33.  Determination  of  the  Centers  of  the  Internal  Surfaces 68 

34.  Direct  Determination  of  the  Radii 70 

35.  General  Remarks 71 

Bibliography 72 


CHAPTER  V 
CIRCLES  OF  DIFFUSION 

36.  Definition 73 

37.  Line  of  Sight 74 

38.  Accommodation 74 

39.  Experiment  of  Czermack,  Schemer  and  Mile 75 

40.  The  Optometer  of  Thomas  Young 75 

41.  Effects  of  the  Stenopaic  Opening 77 

Bibliography 0 78 

CHAPTER  VI 
ANOMALIES  OF  REFRACTION 

42.  General  Remarks 79 

43.  General  Remarks  on  Ametropia So 

44.  Optometers 83 

45.  Myopia 84 

46.  Choice  of  Spectacles 87 

47.  Treatment  of  Myopia 88 

48.  Hypermetropia 9° 

49.  Aphakia 92 

Bibliography 94 


CHAPTER  VII 
SPHERICAL  ABERRATION 

PAGE 

50.  Optic  Principles , 95 

51.  Phenomena  Dependent  on  the  Spherical  Aberration  of  Lenses 96 

52.  Aberration  of  the  Human  Eye.     Experiments  of  Volkmann loo 

53.  Experiments  of  Thomas  Young 101 

Bibliography  .....    l( 108 

CHAPTER  VIII 

CHROMATIC  ABERRATION 

54.  Optic  Principles 109 

55.  Chromatic  Aberration  of  the  Eye Ill 

56.  Experiment  of  Wollaston ill 

57.  Results 112 

58.  Phenomena  of  Dispersion,  the  Pupil  being  Partly  Covered 113 

59.  Correction  of  Chromatic  Aberration 114 

Bibliography 114 

CHAPTER  IX 
REGULAR  ASTIGMATISM 

60.  Optic  Principles.     Astigmatism  Produced  by  the  Form  of  the  Surfaces 115 

61.  Defects  of  the  Image 118 

62.  Astigmatic  Surfaces 118 

63.  Astigmatism  by  Incidence 119 

64.  Astigmatism  of  the  Human  Eye.     Historical 12 1 

65.  Physiologic  Astigmatism 122 

66.  Corneal  Astigmatism 122 

67.  Measurement  of  the  Corneal  Astigmatism 123 

68.  Regular  Corneal  Astigmatism 125 

69.  Relations  between  Ophthalmometric  and  Subjective  Astigmatisms 125 

70.  Astigmatic  Accommodation 129 

71.  Post-Operative  Astigmatism 130 

72.  Keratoconus 131 

73.  Symptoms  of  Astigmatism 132 

74.  Examination  of  Astigmatic  Patients   . 133 

Bibliography 136 

CHAPTER  X 
IRREGULAR  ASTIGMATISM 

75.  General  Remarks 137 

76.  Examination  of  the  Eye  with  a  Luminous  Point ,    .        .  138 

77.  Different  Forms  of  Irregular  Astigmatism ....  139 

78.  Rules  for  Analyzing  the  Figures  of  the  Luminous  Point 143 

Bibliography 146 


CHAPTER  XI 
ENTOPTIC  PHENOMENA 

PAGE 

79.  Manner  of  Observing  Entoptic  Phenomena 147 

80.  Analysis  of  Entoptic  Phenomena 151 

81.  Entoptic  Observation  of  the  Vessels  of  the  Retina 153 

82.  Other  Entoptic  Phenomena 156 

Bibliography 159 

CHAPTER  XII 
ACCOMMODATION 

83.  Measurement  of  the  Amplitude  of  Accommodation 160 

84.  Mechanism  of  Accommodation  (Historical,  A.) t 162 

85.  Mechanism  of  Accommodation  (Historical,  B.) 167 

86.  Personal  Experiments I71 

87.  The  Author's  Theory  of  Accommodation 183 

Bibliography 189 

CHAPTER  XIII 
OPHTHALMOSCOPY 

88.  Methods  of  Illuminating  the  Fundus  of  the  Eye 190 

89.  Examination  by  the  Erect  Image 193 

90.  Examination  by  the  Erect  Image.     Observations 197 

91.  Examination  by  the  Inverted  Image „    , 200 

92.  Ophthalmoscopic  Examination  of  the  Refracting  Media 204 

93.  Skiascopy 205 

Bibliography   .    , c 210 

CHAPTER  XIV 

THE  PUPIL 

94.  General  Remarks 211 

95.  Action  of  Mydriatics  and  of  Myotics 212 

96.  Movements  of  the  Pupil .»...'. 2I2 

97.  Advantage  of  the  Position  of  the  Pupil  near  the  Nodal  Point  . 215 

Bibliography  .   .  „ <    .        . 220 


BOOK  II 

FUNCTIONS  OF  THE  RETINA 


CHAPTER  XV 

CHANGES  WHICH   THE   RETINA  UNDERGOES  UNDER  THE 
INFLUENCE  OF  LIGHT 

PAGE 

98.  Retinal  Purple .221 

99.  Movements  of  the  Pigment  Under,  the  Influence  of  Light 222 

Bibliography 223 

CHAPTER  XVI 
THE  LIGHT  SENSE 

100.  Psychophysical  Law  of  Fechner 224 

101.  Measurement  of  the  Light  Sense 228 

102.  Results 231 

Bibliography 233 

CHAPTER  XVII 
THE  COLOR  SENSE 

103.  General  Remarks 234 

104.  Phenomena  of  Contrast  (Simultaneous) ....  238 

105.  After  Images 241 

106.  Phenomena  Dependent  on  the  Variation  of  the  Brightness  of  the  Colors 243 

107.  Methods  of  Mixing  the  Colors 247 

108.  Results  of  the  Mixtures  of  Colors 250 

109.  Abnormal  Trichromasia „ 261 

no.   Color  Blindness  or  Daltonism  (Dichromasia) 263 

111.  Monochromasia .  269 

112.  Clinical  Examination  of  the  Color  Sense 269 

113.  Hypotheses  on  the  Mechanism  of  Color  Vision .    .  272 

Bibliography .•••»••••*••-,«        ......  275 


CHAPTER  XVIII 
THE  FORM  SENSE 

114.  Central  Visual  Acuity 277 

115.  Peripheral  Acuity 282 

Bibliography 286 


BOOK  III 

THE   OCULAR  MOVEMENTS   AND   BINOCULAR   VISION 


CHAPTER  XIX 
THE   LAW   OF   LISTING 

PAGE 

116.  Centers  and  Axes  of  Rotation  of  the  Eye 287 

117.  Law  of  Listing 289 

118.  Experiments  of  Meissner.     Apparently  Vertical  Meridian 294 

119.  Historical 297 

Bibliography 298 

CHAPTER  XX 
THE   OCULAR   MOVEMENTS 

120.  Jerking  Movements  of  the  Eyes 299 

121.  Relative  Movements  of  the  Two  Eyes 299 

122.  Measurement  of  Convergence 301 

123.  Relations  between  Accommodation  and  Convergence 303 

Bibliography  ...,..„.., 303 

CHAPTER  XXI 
PROJECTION  OF  VISUAL  IMPRESSIONS 

124.  Projection  Outwards  of  Uniocular  Vision 304 

125.  Projection  of  the  Visual  Field 304 

126.  Projection  in  Binocular  Vision 307 

Bibliography 312 

CHAPTER  XXII 
MONOCULAR  PERCEPTION  OF  DEPTH 

127.  Influence  of  Accommodation 313 

128.  Indirect  Judgment  of  Distance 313 

129.  Influence  of  the  Parallax 315 

Bibliography 3l6 

CHAPTER  XXIII 
BINOCULAR  PERCEPTION  OF  DEPTH 

130.  Influence  of  Convergence 3*7 

131.  The  Stereoscope 31/ 

132.  Effect  of  the  Stereoscope 322 

133.  Identical  Points  of  the  Retince 324 

Bibliography 32^ 


CHAPTER  XXIV 
STRABISMUS 

PAGE 

134.  Different  forms  of  Strabismus 329 

135.  Measurement  of  Strabismus 

136.  Etiology  of  Concomitant  Strabismus 

137.  Vision  of  Strabismic  Patients 

138.  Treatment  of  Strabismus 335 

Bibliography •     337 

CHAPTER  XXV   ^ 
OPTIC   ILLUSIONS 

139.  Optic  Illusions 338 

Bibliography 34 

Treatises  to  Consult 343 


LIST  OF  ILLUSTRATIONS 


FIG.  PAGE 

Frontispiece — Portrait  of  the  Author 

1.  Luminous  Source,  Opaque  Body,  Shadow  and  Penumbra I 

2.  Reflection  on  a  Plane  Mirror 3 

3.  Reflection  on  a  Concave  Mirror 4 

4.  Reflection  on  a  Concave  Mirror 4 

5.  Reflection  on  a  Convex  Mirror 6 

6.  Construction  of  the  Utilized  Part  of  a  Mirror 7 

7.  Refraction 8 

8.  Total  Reflection 9 

9.  Prism  with  Total  Reflection 9 

10.  Refraction  by  a  Plate  with  Plane  Parallel  Surfaces IO 

11.  Refraction  by  a  Prism IO 

12.  Refraction  by  a  Spherical  Surface II 

13.  Refraction  by  a  Spherical  Surface 12 

14.  Refraction  by  a  Parabolic  Surface 13 

15.  Construction  of  Image  Formed  by  a  Thin  Lens 15 

16.  Method  of  Measuring  the  Focal  Distance  of  a  Lens       17 

17.  Principal  and  Nodal  Points  ;  Anterior  and  Posterior  Focus 19 

18.  Construction  of  the  Image  of  an  Object 20 

19.  Construction  to  Find  the  Second  Principal  Plane 21 

19  a.  Construction  of  the  Cardinal  Points  of  Two  Optic  Systems 22 

20.  Construction  to  Find  the  Nodal  Points  of  a  Thick  Lens 23 

21.  Optic  System  of  the  Eye 27 

22.  Optic  System  of  the  Eye  of  an  Ox 28 

23.  Images  of  Purkinje  of  the  Eye  of  an  Ox  (Dead) 29 

24.  Double  Crystalline  Images  in  a  Case  of  False  Lenticonus 29 

25.  Diagram  of  the  Crystalline  Lens 30 

26.  Position  of  the  Cardinal  Points  of  the  Human  Eye 32 

27.  Pupil  of  Entrance  and  Pupil  of  Exit 35 

28.  Reflections  and  Refractions  by  a  Lens       39 

29.  Manner  in  which  a  Luminous  Ray  is  Divided  in  the  Eye 40 

30.  Position  of  the  Seven  Images  in  the  Eye 41 

31.  Corneal  Images  of  two  Lamps  Observed  with  the  Ophthalmophakometer 43 

32.  The  Ophthalmophakometer 44 

33.  Illustration  of  the  Principle  of  Doubling 48 

34.  Doubling  by  the  Two  Halves  of  an  Objective 49 

35.  Plates  of  Helmholtz 49 

36.  Doubling  by  an  Objective,  a  Central  Vertical  Band  of  which  has  been  Removed  .    .  50 

37.  Prism  of  Wollaston 50 

38.  Ophthalmometer  of  Javal  and  Schioetz S1 

39.  Images  of  the  Mires  Seen  Doubled .  52 

40.  Refraction  by  a  Conical  Cornea 54 

41.  Radii  of  Curvature  of  the  Cornea 55 

42.  Diagram  of  Corneal  Refraction 57 

43.  Forms  of  the  Image  of  a  White  Square  at  Different  Parts  of  the  Cornea 5& 

44.  Keratoscopic  Images  of  an  Astigmatic  Cornea 60 

45.  Keratoscopic  Images  of  an  Astigmatic  Cornea 61 

46.  Keratoscopic  Images  of  a  Case  of  Keratoconus 62 

46  a.  Keratoscopic  Image  of  an  Eye  with  a  Large  Angle  a 63 

46  <J.  Spot  of  Mariotte  of  an  Eye  with  a  Large  Angle  a 63 


47.  The  Ophthalmophakometer 64 

48.  The  Images  of  Purkinje  Observed  with  the  Ophthalmophakometer 64 

49.  Position  of  the  Images  of  Purkinje,  the  Lamps  being  Arranged  Vertically  ....  65 

50.  Position  of  the  Images  of  Purkinje,  the  Lamps  being  Arranged  Horizontally    .    .  65 

51.  Defect  of  Centering  ;  Alignment  of  the  Images  Impossible 66 

52.  Determining  the  Position  of  an  Internal  Surface  of  the  Eye 68 

53.  Determining  the  Position  of  an  Internal  Surface  of  the  Eye 69 

54.  Calculation  of  the  Size  of  the  Circle  of  Diffusion 73 

55.  Rules  of  the  Optometer  of  Young 76 

56.  Magnification  by  Means  of  the  Stenopaic  Opening 77 

57.  Retinal  Image  in  Myopia  and  Hypermetropia 82 

58.  Principle  of  Badal 84 

59.  Size  of  Retinal  Image  when  the  Focus  of  the  Lens  Coincides  with  the  Anterior 

Focus  of  the  Eye 84 

60.  Distribution  of  the  Anomalies  of  Refraction 85 

61.  Refraction  of  a  Pencil  of  Parallel  Rays  by  a  Spherical  Surface 95 

62.  Spherical  Aberration  of  a  Lens 97 

63.  Deformity  of  the  Shadows  of  the  Needles 98 

64.  Experiment  of  Volkmann loo 

65.  Distribution  of  the  Light  of  the  Circle  of  Diffusion 101 

66.  The  Aberroscope 102 

67.  The  Rules  of  the  Optometer  of  Young 102 

68.  The  Appearance  Assumed  by  the  Line  of  the  Optometer  of  Young 103 

69.  Deformity  of  the  Shadows  in  an  Eye  with  Strong  Spherical  Aberration 105 

70.  Aberration  Over-Corrected  Towards  the  Borders 106 

71.  Aberration  Over-Corrected  Above 106 

72.  Aberration  Over- Corrected  Everywhere 1 06 

72*2.  Stadfeldt's  Instrument  for  Measuring  Aberration  of  the  Crystalline  Lens  (Dead)  107 

73.  Achromatic  Prism no 

74.  Prism  a  vision  directe no 

75.  Chromatic  Aberration  of  the  Eye 112 

76.  Phenomena  of  Dispersion 113 

77.  Circles  of  Diffusion  and  Focal  Lines  of  a  Regularly  Astigmatic  System 115 

78.  Focal  Lines  of  a  Regularly  Astigmatic  System 116 

79.  Construction  of  the  Elliptical  Diffusion  Spot 117 

80.  A  Torus 119 

81.  Focal  Line  of  Lens  Placed  Obliquely 120 

82.  Astigmatism  by  Incidence  ;  Focal  Lines 120 

83.  Explanation  of  the  Difference  in  Level  (denivellation)* 123 

84.  Keratoscopic  Images  of  a  Case  of  Keratoconus 131 

85.  Forms  Under  which  a  Luminous  Point  is  Seen  by  a  Regular  Eye 139 

86.  In  Regular  Astigmatism  with  Spherical  Aberration 140 

87.  Figures  of  a  Luminous  Point  Obtained  by  Combining  a  Spherical  with  a  Cylindri- 

cal Lens 140 

88.  Forms  which  a  Luminous  Point  Presents  to  the  Author's  Right  Eye 141 

89.  To  an  Eye  with  Double  Obliquity 141 

90.  Figures  of  the  Left  Eye  of  M.  Ree 142 

91.  Curved  Focal  Line 142 

92.  Irregular  Eye  (Diplopia) 143 

93.  Aberroscopic  Phenomena 145 

94.  Diagram  of  Variations  of  Refraction  in  the  Pupil 145 

95.  Course  of  the  Rays  in  the  Author's  Right  Eye 146 

96.  Specks  on  the  Anterior  Surface  of  the  Cornea 148 

97.  Striae  Produced  by  Winking 148 

98.  Prismatic  Effect  of  the  Layer  of  Tears 148 

99.  Speckled  Appearance  of  the  Entoptic  Field  Produced  by  Rubbing  the  Cornea  .  .  149 

100.  Star  Figure  of  the  Crystalline  Lens 149 

101.  Incipient  Cataract  Seen  Entoptically 149 


*[This  figure  83  does  not  quite  illustrate  the  actual  picture  that  we  obtain  by  looking  at  the  cornea!  images  K 
and  L  with  the  ophthalmometer.  For  with  the  Wollaston  prism  K  is  not  seen  any  more,  but  instead  of  it  we 
observe  Ka  at  the  place  indicated  in  the  figure,  and  Ka  at  a  distance,  K  Kj  to  the  left  of  K  in  the  direction  of 
doubling  ot  the  prism.  The  same  is  the  case  with  Lt,  only  that  L2  is  displaced  to  the  right.  But  to  avoid  com- 
plication the  two  images  Ka  and  L3  have  been  omitted.]  W. 


FIG.  PAGE 

101  a.  The  Eatoptoscope 150 

102.  Parallax  of  the  Entoptic  Phenomena 151 

103.  Determination  of  the  Position  of  an  Entoptic  Object 152 

104.  Entoptic  Luminous  Image  Surrounded  by  a  Shadow 153 

105.  Entoptic  Observation  of  the  Vessels  .    . 154 

106.  Entoptic  Observation  of  the  Vessels 155 

io6a.  Entoptic  Phenomenon 158 

107.  Centripetal  Movement  of  the  Catoptric  Image 164 

108.  Putting  the  Eye  Under  Water 168 

109.  Ciliary  Muscle  of  Man 169 

no.  Ciliary  Part  of  the  Eye  of  a  Cat 170 

111.  Change  of  Aberroscopic  Phenomena  During  Accommodation 171 

112.  Appearance  of  the  Luminous  Point 172 

113.  Appearance  of  the  Luminous  Point 173 

1 130.  Slciascopic  Examination  of  Accommodation 175 

114.  Reflection  Images  of  the  Eye 176 

115.  Reflection  Images  of  the  Eye 176 

116.  Reflection  Images  of  the  Eye 177 

117.  Deformity  of  the  Corneal  Image  of  a  White  Square  in  a  Case  of  Keratoconus  .    .  177 

118.  Refraction  by  a  Parabolic  Surface 178 

119.  Deformity  of  the  Crystalline  Surfaces  During  Accommodation 179 

1 20.  Accommodative  Phenomena  of  the  Eye 180 

121.  Accommodative  Phenomena  of  the  Eye 180 

122.  Change  of  the  Anterior  Chamber  During  Accommodation 182 

122  a.  Reflection  Images  on  the  Anterior  Surfaces  of  the  Dead  Crystalline  Lens  ....  183 

122  b.  The  Dead  Crystalline  Lens  and  the  Accommodated  Crystalline  Lens 184 

123.  Crystalline  Lens  of  the  Ox 185 

124.  Optic  System  of  the  Eye  of  the  Ox ,    .  186 

125.  Illumination  of  the  Fundus  by  a  Light  for  which  the  Eye  is  Accommodated  .    .    .  190 

126.  Illumination  of  the  Fundus  by  a  Light  for  which  the  Eye  is  Not  Accommodated .  191 

127.  Principle  of  the  Ophthalmoscope  of  Helmholtz 192 

128.  Magnification  of  the  Fundus,  both  Patient  and  Observer  being  Emmetropic  .    .    .  194 

129.  Line  of  Image  of  Papilla  if  the  Fundus  of  Patient  is  Placed  Free  in  the  Air.  .    .  195 

130.  Magnification  of  Fundus  if  Patient  is  Myopic 195 

131.  Construction  of  the  Ophthalmoscopic  Field 196 

132.  Magnification  by  the  Inverted  Image  in  Emmetropia 201 

133.  Influence  of  Refraction  of  the  Examined  Eye  on  the  Magnification  if  Focus  of 

Lens  Coincides  with  Anterior  Focus  of  Eye 2OI 

134.  Influence  of   Refraction  of   the   Examined  Eye  on  the  Magnification  if  Lens  is 

Nearer  to  the  Eye  than  in  Fig.  133 202 

135.  Construction  of  the  Ophthalmoscopic  Field  by  the  Inverted  Image 203 

136.  Skiascopy.     Plane  Mirror 205 

137.  Skiascopy.     Concave  Mirror 206 

138.  Boundaries  of  the  Skiascopic  Field 207 

139.  Theory  of  Leroy 208 

140.  Theory  of  Leroy 208 

141.  Theory  of  the  Paracentral  Shadow 209 

142.  The  Advantage  of  the  Position  of  the  Pupil  Near  the  Nodal  Point 215 

143.  Experiment  of  Helmholtz 2i6 

144.  Hyperbolic  Chessboard  of  Helmholtz 217 

145.  Artificial  Eye 218 

146.  Image  of  a  Window  in  the  Artificial  Eye 218 

146  a.  Section  of  the  Retina  of  a  Frog 223 

147.  Experiment  of  Bouger 225 

148.  Curve  Showing  the  Relation  between  the  Light  Sense  and  the  Illumination  .    .    .  227 

149.  Photoptometer  of  Foerster 228 

150.  Disc  of  Masson 229 

150  a.  Disc  of  Helmholtz  and  Disc  of  Benham 230 

151.  Spectrum  of  Refraction;  Spectrum  of  Diffraction 235 

152.  Table  of  Colors  after  Newton 237 

153.  Experiment  of  Ragona  Scina 239 

154.  Experiment  with  Colored  Shadows 240 

155.  Disc  of  Masson 241 

156.  Curves  of  Parinaud  to  Show  the  Threshold  for  Different  Rays  of  the  Spectrum  .  .  246 


FIG.  PAGR 

157.  Color  Box  of  Maxwell 248 

158.  Mixture  of  Colors  by  Means  of  a  Glass  Plate 249 

159.  Table  of  Colors  after  Newton 250 

1 60.  Color  Table  of  Maxwell 252 

161.  "Color  Box"  of  Maxwell 253 

162.  Color  Curves  of  Maxwell 254 

163.  Color  Table  of  Maxwell 256 

164.  Color  Table  of  Helmholtz 260 

165.  Color  Table  of  Maxwell 265 

166.  Color  Curves  of  a  Dichromatic 267 

167.  Color  Table  of  a  Dichromatic 267 

1 68.  Chromatoptometer  of  Chibret 271 

169.  Experiment  of  Hooke 278 

170.  Measurement  of  the  Visual  Acuity  by  a  Grating 278 

171.  Measurement  of  the  Visual  Acuity  by  a  Grating 278 

172.  Experiment  of  Hooke,  the  Optics  of  the  Eye  being  Defective 278 

173.  Mariotte's  Blind  Spot 284 

174.  Phenomenon  of  Troxler 285 

175.  Determination  of  the  Center  of  Rotation  of  the  Eye 288 

176.  The  Two  Axes  of  Rotation  Lying  in  the  Horizontal  Plane 288 

177.  Demonstration  of  the  Law  of  Listing 290 

178.  Demonstration  of  the  Law  of  Listing 291 

179.  Demonstration  of  the  Law  of  Listing 292 

180.  Discs  of  Volkmann 295 

181.  Modification  of  the  Experiment  of  Meissner 296 

182.  Illustration  of  the  Meter  Angle : 302 

183.  Explanation  of  Binocular  Physiologic  Diplopia 308 

184.  Experiment  to  Find  the  Center  of  Projection 310 

185.  Horopter  of  Johannes  Muller 311 

186.  Apparent  Form  of  the  Sky 315 

187.  Influence  of  Parallax  for  Stereoscopic  Vision 316 

188.  Principle  of  Stereoscopic  Images 318 

189.  Stereoscope  of  Wheatstone 320 

190.  Pseudoscope  of  Wheatstone 320 

191.  Telestereoscope  of  Helmholtz 321 

192.  Binocular  Ophthalmoscope 322 

193.  Antagonism  of  the  Visual  Fields 324 

194.  Suppression  of  one  of  the  Images  in  Stereoscopic  Vision 327 

195  to  201.     Optic  Illusions 


XVI 


PHYSIOLOGIC  OPTICS 


BOOK   I 


OCULAR  DIOPTRICS 


CHAPTER  I 

OPTIC  PRINCIPLES 

1.  Optic  Properties  of  Bodies.  —  Bodies  are  of  three  kinds :  transparent 
bodies,  through  which  we  can  see  objects,  translucent  bodies  such  as 
ground  glass,  through  which  we  perceive  light,  but  cannot  distinguish 
form,  and  opaque  bodies.  —  No  body  is  absolutely  transparent.  Pure 
water  is  transparent,  but  very  little  light  will  pass  through  a  great  thick- 
ness of  water.  —  On  the  contrary  very  thin  layers  of  opaque  substances 


Fig.  1.  —  A,  luminous  source ;  B,  opaque  body ;  C,  shadow ;  D,  penumbra. 

are  more  or  less  translucent,  as  all  know  who  have  examined  micro- 
scopic preparations. 

2.  Rectilinear  Propagation  of  Light.  —  In  a  homogeneous  medium 
light  is  propagated  along  straight  lines  which  are  called  luminous  rays. 

SHADOWS.  —  When  rays  emanating  from  a  luminous  point  fall  upon 
an  opaque  body  there  is  produced  behind  the  latter  a  shadow  which  is 
conical  in  shape.  We  can  construct  the  form  of  this  shadow  by  drawing 
straight  lines  joining  the  different  points  of  the  border  of  the  body  with 


2  PHYSIOLOGIC  OPTICS 

the  luminous  point.  If,  instead  of  a  point,  the  source  is  a  luminous  sur- 
face the  shadow  is  surrounded  by  a  penumbra,  the  intensity  of  which 
diminishes  more  and  more  towards  the  periphery.  An  observer  placed 
in  the  shadow  C  could  not  see  any  point  of  the  luminous  surface;  placed 
in  the  penumbra  D  he  would  see  a  part  of  that  surface,  greater  in  pro- 
portion as  he  approaches  the  border. 

IMAGES  PRODUCED  BY  A  SMALL  APERTURE.  —  Rays  passing  through 
a  small  aperture  into  a  dark  room  form  on  a  screen  an  inverted  image 
of  exterior  objects.  By  diminishing  the  aperture  the  image  gains  in  dis- 
tinctness, but  loses  in  luminosity.  Photographs  may  be  taken  in  this 
way. 

3.  Beflection  and  Absorption.  —  Rays  which  strike  the  surface  of  an 
opaque  object  are  partly  absorbed  and  partly  reflected.    If  the  surface  is 
not  polished  the  rays  are  reflected  in  a  diffuse  manner :  each  point  of  the 
surface  sends  back  light  in  all  directions.     It  is  through  the  agency  of 
this  irregularly  reflected  light  that  objects  are  visible,  and  the  fact  that 
they  are  visible,  whatever  may  be  the  position  of  the  observer,  provided 
the  rays  are  not  intercepted,  proves  conclusively  that  any  point  whatever 
of  the  surface  sends  rays  in  all  directions. 

4.  Regular  Reflection.  —  The  more  polished  the  surface  the  less  dif- 
fuse is  the  reflection.    Thus  the  surface  of  a  highly  polished  mirror  is  but 
slightly  visible.    Polished  surfaces  reflect  rays  regularly  following  a  law 
which  was 'known  from  remote  ages,  viz.,  that  the  reflected  ray  is  in  the 
same  plane  with  the  incident  ray  and  the  normal  to  the  point  of  incidence, 
and  that  both  rays  form  equal  angles  with  the  normal,  which  is  expressed 
by  saying  that  the  angle  of  incidence  and  the  angle  of  reflection  are  equal. 

The  effect  of  this  reflection  is  to  produce  images  of  external  objects. 
The  image  of  a  point  is  the  place  where  the  rays  which  emanated  from 
that  point  meet  again  after  reflection  or  refraction.  In  order  that  the 
image  may  be  perfect,  all  the  rays  employed  should  meet  in  a  point.  Gen- 
erally this  condition  is  not  quite  fulfilled,  there  being  more  or  less  pro- 
nounced aberrations.  —  A  point  and  the  image  of  this  point  we  designate 
as  conjugate  points.  —  An  image  is  real  when  the  rays  proceeding  from 
a  point  meet  again  in  a  point ;  it  is  virtual  when  it  is  formed  not  by  the 
reunion  of  the  rays  themselves,  but  of  their  prolongations.  —  A  real 
image  can  be  received  on  a  screen;  a  virtual  image  cannot,  but  it  is  visi- 
ble to  the  eye  which  is  in  the  path  of  the  rays  because  the  optic  system 


OPTIC  PRINCIPLES 


A' 


of  the  eye  forms  a  real  image  of  it  on  the  retina,  exactly  as  if  the  virtual 
image  was  an  object. 

5.  Plane  Mirrors.    Construction  of  the  Image.  —  Let  fall  from  a  point 
A  (fig.  2)   of  the  object  a  perpendicular  AB  on  the  surface,  DE,  of  the 
mirror,  and  mark  on  its  prolongation  a  point  A'  so  that  AB  is  equal  to 
A'B.    A'  is  the  image  of 

A,  for  since  AB  =  A'B, 
the  two  angles  «  are 
equal,  and  consequently 
also  the  two  angles  i, 
each  of  which  is  equal 
90°  —  a.  The  image 
formed  by  a  plane  mirror 
is  virtual,  erect  and  equal 
in  size  to  the  object. 

To  tell  whether  a  mir- 
ror is  true  place  the  eye 
near  the  surface  by  way 
of  observing  images  un- 
der as  great  an  incidence 
as  possible.  If  the  mir- 
ror is  not  true  the  images 

of  external  objects  are  deformed.  One  can  also  notice  these  deformities 
very  distinctly  by  placing  oneself  quite  a  distance  in  front  of  the  mirror 
and  observing  the  images  of  distant  objects. 

6.  Concave  Spherical  Mirrors.  —  The  middle  of  the  spherical  surface 
is  called  the  apex,  a  straight  line  passing  through  the  center  and  the  apex 
is  the  axis,  and  the  angular  measurement  of  the  mirror  is  the  aperture. 
In  order  that  images  may  be  true  the  aperture  must  be  small  (8  to  9  de- 
grees).   The  principal  focus  of  the  mirror  is  the  place  where  incident  rays 
parallel  to  the  axis  meet  after  reflection.    The  principal  focal  distance  is. 
the  distance  of  the  principal  focus  from  the  mirror. 

IN  ALL  OPTIC  PHENOMENA  THE  COURSE  OF  THE  RAYS  is  REVERSI- 
BLE. —  If  in  figure  2,  the  ray  AC  is  reflected  along  CF,  an  incident  ray- 
along  FC  is  reflected  along  CA.— It  follows  that  rays  coming  from  the 
principal  focus  of  a  concave  mirror  must  be  parallel  after  reflection. 

The  principal  focus  of  a  plane  mirror  is  at  infinity,  because  incident 
parallel  rays  are  still  parallel  after  reflection. 


Fig.  2.  —  Keflection  on  a  plane  mirror.  A,  the  object ; 
A',  its  image;  DE,  the  mirror;  AC,  incident  ray;  CF, 
reflected  ray. 


PHYSIOLOGIC   OPTICS 


The  principal  focus  of  a  concave  mirror  is  situated  half  way  between 

v  the  apex  and  center.  We  have,  indeed 

— ->  \         *  =  *  (fig.  3),  since  the  angles  of  inci- 

dence and  reflection  are  equal,  and 
i  =  BC<£  because  the  incident  ray  is 
parallel  to  the  axis.  It  follows  that 
C<£  =  B<£,  but  as  the  aperture  is 
'  very  small,  we  can  consider  B<f>  = 

Fig.  3.  —  Reflection  on  a  concave  mirror.      Q<&,  therefore   C<£  =   Q4>   =    -J-  ,  if 
C,  the  center;  *,  the  focus.  we  designate  the  radius  fcy  R 


Fig.  4.  — Reflection  on  a  concave  mirror.     Constructions  of  the  image,  I,  of  an  object  O; 
C,  the  center;  *,  the  focus.    AS  =  /t,  A'S  =  f2,  S$  =  F,  A<i>  =  llt  A'$  =  12. 

A  ray  passing  through  the  center  is  perpendicular  to  the  surface;  it 
is  consequently  reflected  on  itself. 


OPTIC  PRINCIPLES  5 

CONSTRUCTION  OF  THE  IMAGE.  —  To  find  the  image  Bj  of  a  point  B 
(fig.  4),  it  suffices  to  trace  the  course  of  two  rays  which  have  emanated 
from  that  point;  the  image  must  be  at  the  place  where  they  intersect  after 
reflection.  After  what  has  been  previously  stated  we  already  know  the 
course  of  three  rays  proceeding  from  the  point  B. 

i°.  The  ray  BM,  which  is  parallel  to  the  axis,  passes  after  reflection 
through  the  focus  <J>; 

2°.  The  ray  B<J>,  which  passes  through  the  focus,  is  reflected  parallel 
to  the  axis  since  the  course  of  the  rays  is  reversible; 

3°.  The  ray  BC,  passing  through  the  center,  is  reflected  on  itself. 

Two  of  these  rays  suffice  for  the  construction.  By  combining  them, 
two  by  two,  we  obtain  the  three  different  constructions  shown  in  figure  4. 

SIZE  OF  THE  IMAGE.  RELATIONS  BETWEEN  THE  DISTANCES  OF  CON- 
JUGATE POINTS. — Let  us  consider  the  line  BA  =  O  (fig.  40)  as  the  object ; 
I  is  its  image.  And  supposing  SL  =  I  and  MS  —  O,  the  triangles  AB4> 
and  SL4>  on  one  side,  and  the  triangles  SM3>  and  A'B'4>  on  the  other 
give  us  the  relations 

°.  =  i.  =  ^  or  /!  I,  =  FF  (Neu-lnn)\ 

The  formula 

_  =  -JL  can  also  be  written  —  =  — -1 ; 
I          r  IK 

which  is  the  formula  we  use  later  in  ophthalmometry.  —  As  we  have 
/!  =  f1  —  F  and   Iz  =  f2  —  F,  the  formula  of  Newton 

/i  k  =  FF 
can  also  be  written 

F    .    F  111 

Tf  +  TT  lorA  +  7r=F 

The  first  of  these  two  formulas  is  that  of  HclmMts;  and,  as  we  shall 
see,  it  is  altogether  general.  The  second  is  identical  with  that  of  infinitely 
thin  lenses. 


(1)  In  this  formula  and  those  which  follow  I  designate  by: 

0,  the  object; 

1,  the  image; 

RI,  the  radius  of  the  first  surface; 

R2,  the  radius  of  the  second  surface; 

FI,  the  anterior  focal  distance; 

Fo,  the  posterior  focal  distance; 

fi,  the  distance  of  the  object  from  the  surface; 

f«,  the  distance  of  the  image  from  the  surface; 

ti,  the  distance  of  the  object  from  the  anterior  focus; 

?2.  the  distance  of  the  image  from  the  posterior  focus; 

For  mirrors  and  lenses  surrounded  with  the  same  media  on  both  sides  we  have  F!  =  F2  =  F 


6  PHYSIOLOGIC   OPTICS 

By  construction  or  formula  we  find  that: 

i°.  The  image  of  an  object  placed  beyond  the  center  is  situated  be- 
tween the  center  and  focus.  It  is  real,  inverted  and  diminished; 

2° .  As  the  course  of  the  rays  is  reversible,  an  object  placed  between 
the  center  and  the  focus  gives  an  image  situated  beyond  the  center,  and 
this  image  is  real,  inverted  and  enlarged; 

3°.  An  object  placed  between  the  focus  and  the  mirror  forms  its  image 
behind  the  mirror.  This  image  is  virtual,  erect  and  enlarged. 

7.  Convex  Mirrors.  —  As  in  the  case  of  concave  mirrors,  the  focus  is 
placed  at  an  equal  distance  between  the  surface  and  center.  The  con- 
struction (fig.  5)  is  the  same  as  in  the  preceding  case,  and  the  formulae 


Fig.  5.  —  Reflection  on  a  convex  mirror.     Construction  of  the  image.     C,  the  center; 

$,  the  focus. 

also,  but  the  distances  of  the  points  situated  behind  the  surface  must  be 
considered  as  negative;  we  have  therefore 


The  image  of  a  real  object  is  always  virtual,  erect  and  diminished;  it  is 
situated  between  the  surface  and  the  focus. 

8.  Practical  Remarks.  —  One  can  tell  whether  a  mirror  is  convex,  con- 
cave or  plane  by  placing  the  eye  near  the  surface.   A  convex  mirror  forms 
a  diminished  image  of  the  eye,  a  concave  mirror  gives  a  magnified  image 
(provided  the  eye  is  between  the  focus  and  the  mirror).     The  image 
formed  by  a  plane  mirror  is  the  same  size  as  the  object. 
To  determine  the  focal  distance  of  a  concave  mirror  we  can  : 
i.  Form  the  image  of  a  distant  object  on  a  screen:  the  distance  of  the 
mirror  from  the  screen  is  equal  to  the  focal  distance  ; 


OPTIC  PRINCIPLES  7 

2.  Place  the  screen  by  the  side  of  a  flame  and  find  the  distance  from  the 
mirror  at  which  the  image  appears  distinct.  The  distance  of  the  mirror 
from  the  flame  is  double  the  focal  distance,  for  since  the  object  and  image 
are,  in  this  case,  at  the  same  distance  from  the  mirror,  this  distance  is 
equal  to  the  radius  of  the  mirror  or  double  its  focal  distance.  We  de- 
termine the  focal  distance  of  a  convex  mirror  by  finding  the  position  of  the 
screen  at  which  the  reflex  which  the  mirror  forms  of  a  distant  flame  has 
a  diameter  equal  to  double  the  diameter  of  the  mirror.  The  distance  of 
the  mirror  from  the  screen  is  equal  to  the  focal  distance,  as  a  simple 
geometrical  construction  will  show. — For  all  small  mirrors  ophthalmo- 
metric  processes  are  used. 

Concave  mirrors,  like  convex  lenses,  make  rays  converge,  while  con- 
vex mirrors  make  them  diverge.  For  this  reason  convex  mirrors  are 
used  as  ophthalmoscopes  when  it  is  desirable  to  have  a  very  feeble  light. 

A  combination  of  a  plane  mirror  with  a  convex  lens  acts  like  a  concave 
mirror  with  a  focal  distance  equal  to  that  of  the  lens  or  half  of  it,  accord- 
ing as  the  light  traverses  the  lens  once  or  twice  (ophthalmoscope  of 
Coccius).  A  combination  of  a  plane  mirror  with  a  concave  lens  acts  like 
a  convex  mirror. 

PORTION  OF  MIRRORS  USED.  —  Except  in  the  case  when  an  image  is 
projected  on  a  screen  it  is  only  a  small  part  of  the  mirror  that  is  utilized. 
We  can  find  this  part  by  constructing  the  image  I  (fig.  6)  of  the  object 


Fig.  6.  —  Construction  of  the  utilized  part  AB  of  a  mirror. 

O  and  by  joining  by  straight  lines  its  margin  with  the  margin  of  the 
observer's  pupil.  These  straight  lines  delimit  the  utilized  portion  of  the 
mirror  AB.  We  could  also  construct  the  image  of  the  pupil  and  join  this 
image  to  the  object;  the  result  would  be  the  same. 


PHYSIOLOGIC   OPTICS 


9.  Refraction.  —  When  a  luminous  ray  strikes  n.  polished  surface  sepa- 
rating two  transparent  media  it  is  divided  into  two,  a  reflected  ray  which  is 
thrown  back  into  the  first  medium  and  a  refracted  ray  which  continues 
its  course  in  the  second  (fig.  7).  The  three  rays  are  in  the  same  plane 
which  contains  also  the  normal  to  the  point  of  inci- 
dence. The  angle  of  reflection  is,  as  we  have  seen, 
equal  to  the  angle  of  incidence,  but  the  angle  of 
refraction  (formed  by  the  normal  and  the  refracted 
ray)  is  different.  Its  size  is  determined  by  the  law 
of  Descartes  (Snellius).  The  ratio  between  the  sine  of 
the  angle  of  incidence  and  the  sine  of  the  angle  of  re- 
fraction is  constant,  whatever  may  be  the  angle  of  inci- 
dence, as  long  as  two  media  remain  the  same. 


Fig.  7. 

The  symbol  n  denotes  the  index  of  refraction,  and  the  index  of  air  is 
generally  adopted  as  the  unit.  The  index  of  water  in  relation  to  air  is 
|  =  1.333,  that  of  glass  in  relation  to  air  is  approximately  \  =  Io-  The 
index  of  glass  in  relation  to  water  is,  then,  -|  -l-  £  =  -f ,  etc.  In  the 
formulae  which  follow  n  denotes  the  index  of  the  second  medium  as 
compared  with  that  of  the  first. 

10.  Quantity  of  Reflected  Light.  —  Total  Reflection.  —  The  quantity  of 
light  regularly  reflected  increases  with  the  angle  of  incidence,  with  the 
difference  of  index  between  the  tzvo  media,  and  lastly  with  the  degree  of 
polish  of  the  surface.  In  air  a  highly  polished  glass  surface  reflects  about 
4  per  cent,  of  incident  light,  if  the  angle  of  incidence  is  negligible.  Good 
metallic  mirrors  reflect  about  two-thirds  of  the  incident  light. 

Total  reflection  takes  place  when  light,  propagated  in  a  dense  medium, 
meets  at  a  large  angle  of  incidence  the  surface  which  separates  the  dense 
medium  from  a  rarer  one. 

Let  AB  (fig.  8)  be  the  surface  separating  the  air  from  the  water  and  O 
a  luminous  point  in  the  water.  OD  is  a  ray  which,  on  reaching  the  sur- 
face, is  divided  into  two,  DE  which  is  refracted  and  DF  which  is  re- 
flected and  much  feebler ;  the  next  rays  OG  and  OH  are  equally  divided ; 
the  emerging  ray  is  always  more  and  more  refracted  and  loses  more 
and  more  in  intensity,  while  the  reflected  ray  gains  in  intensity;  and 
when  the  angle  of  incidence  reaches  a  certain  size,  the  emergent  ray 
forms  an  angle  of  90°  with  the  normal,  that  is,  it  glances  along  the  sur- 


OPTIC  PRINCIPLES 


face.  We  designate  as  the  critical  angle  the  angle  of  incidence  which 
corresponds  with  an  angle  of  refraction  of  90°.  In  this  case  sin  r  =  1 ; 
therefore, 


sin   ?, 
sin  r 


=  sin  i  =  n. 


In  our  case  n  =  3/4,  sin  i  =  0.75  and  the  critical  angle  is  about  49°. 
If  the  angle  of  incidence  exceeds  the  critical  angle  all  the  light  is  reflected 
(total  reflection)  (OK,  fig.  8). 


Air 


Fig.  8.— Total  Reflection. 

If  we  pour  water  into  a  glass  and  try  to  look  obliquely  from  below 
upwards  through  the  surface  of  the  water  this  surface  appears  like  an 
absolutely  opaque  metallic  surface.  No  ray  coming  from  above  reaches 
the  eye  because  all  are  deflected  towards  the 
bottom  of  the  glass  by  refraction.  If  we  dip 
a  pencil  in  the  water  we  see  it  mirrored  in 
the  surface;  rays  coming  from  the  pencil 
reach  the  eye  after  total  reflection  at  the  sur- 
face of  the  water. 

As  this  form  of  reflection  is  the  most  com- 
plete of  all,  it  is  frequently  used  in  optic  ex- 
periments. The  most  usual  application  of  it 
is  in  the  rectangular  prism;  looking  per- 
pendicularly at  one  of  the  faces  we  see  an 
image  of  objects  placed  in  front  of  the  other 
face,  formed  by  total  reflection  on  the  hypothenuse  (fig.  9).  Nor  need 
the  prism  be  rectangular;  a  prism  of  60°  gives  a  like  result;  but  in  every 
case  the  three  faces  must  be  polished. 


Fig.  9.  —  Prism  with  total 
reflection. 


10 


PHYSIOLOGIC  OPTICS 


11.  Refraction  by  Plates  with  Plane  and  Parallel  Surfaces.  —  The  inci- 
dent ray  and  the  emergent  ray  are  parallel,  for  we  have  r  =  r  (fig.  10). 

since  the  surfaces  are  parallel,  and 
consequently  also  i  =  i.  The  emerg- 
ent ray  has  suffered  a  displacement 
towards  the  side  whence  the  light 


Fig.  10.  —  Refraction  by  a  plate  with 
plane  and  parallel  surfaces. 


Fig.  11.  —  Refraction  by  a  prism. 


12.  Refraction  by  a  Prism.  —  Seen  through  a  prism  an  object  seems 
deflected  towards  the  apex  of  the  prism.  The  angle  between  the  direc- 
tion along  which  the  object  is  seen  and  that  in  which  it  really  is  found  is 
called  the  deviation.  If  i  (fig.  n)  is  the  angle  of  incidence,  i:  the  angle 
formed  by  the  emergent  ray  with  the  normal,  A  the  angle  of  the  prism. 
and  d  the  deviation,  we  have 


for 
and 
therefore 


d  =  i  +  i1  —  A 

d  =  i  —  r  +  i1  —  rl 

A  =  180°  —  x  =  r  +  r, 

d  =  i  +  i,  —  A. 


The  deviation  is  least  when  i  =  ilf  the  course  of  the  rays  is  then  sym- 
metrical, and  we  have  : 

A  =  2r  and  d  =  2i  —  2r  =  2i  —  A. 

In  the  formula 

sin  i  =  n  sin  r 


we  can  replace  the  sines  by  the  arcs  if  the  latter  are  small;  therefore 


OPTIC  PRINCIPLES  11 

i  =  nr 

and 

d  =  2nr  —  A   ... 

=  (n-l)±.W 

If  the  prism  is  glass,  we  have  n  =    |    approximately,  n  —  I  =    \ 
Therefore  the  deviation  produced  by  a  weak  prism  is  equal  to  half  its  angle. 

13.  Refraction  by  a  Spherical  Surface,  —  Incident  rays  parallel  to  the 
axis  reunite  at  the  posterior  forces  <f>2  (fig.  12).     The  distance  S4>2  is 


Fig.  12.  —  Refraction  by  a  spherical  surface.   4>1(  the  anterior  focus;  4>2,  the  posterior  focus 

C,  the  center. 

known  as  the  posterior  focal  distance;  it  is  expressed  by 


for  we  have 

C$2  _          sin  r 
R.          sin  (i  —  r) 

or,  if  the  angles  are  small, 

C$  r  r  1 


R          i  —  r         nr  —  r         n  —  1 

Therefore 

02  =  -5-_ 

n  —  1 

and 

8*,  -  -5—  +  R  =  -^5_. 


After  refraction  the  rays  coming  from  the  anterior  focus  $±  are  parallel 
to  the  axis.  Its  distance  4>±S  =  Fx  is  called  the  anterior  focal  distance 
and  is  expressed  by 

F  R 

F'-  JT=1' 

indeed,  we  find  this  value  by  a  calculation  analogous  to  that  by  which 
we  have  found  the  posterior  focal  distance. 

(1)  [The  author  here  derives  this  formula  from  that  for  the  least  deviation.  It  may  be  derived  in  a 
more  general  way  thus : 

d  =  i  —  r  +  ii  —  TI  or  for  small  angles 

d  =  nr  —  r  +  nr^  —  n  =  (»  —  1)  (r  +  n)  —  (n  —  1)  A.]-  W. 


1'2  PHYSIOLOGIC   OPTICS 

We  note  that 

F2  =  F!  +  R  =  T.F, 
that  is  to  say: 

i°.  The  difference  between  the  focal  distances  is  equal  to  the  radius; 
2°,  The  ratio  between  the  focal  distances  is  equal  to  the  ratio  between  the 
indices  of  the  corresponding  media. 
3°.  In  fig.  12  we  have 

4>2  S  =  *J  C  =  F2 

The  distance  of  the  center  from  the  posterior  focus  is  equal  to  the  anterior 
focal  distance,  and  the  distance  of  the  center  from  the  anterior  focus  is  equal 
to  the  posterior  focal  distance. 

CONSTRUCTION  OF  THE  IMAGE.  —  To  construct  the  image  of  a  point 
situated  outside  the  axis  we  can  draw : 

i°.  A  ray  passing  through  the  center:  it  is  not  refracted; 

2°.  A  ray  parallel  to  the  axis :  it  is  refracted  towards  the  posterior 
focus ; 

3°.  A  ray  passing  through  the  anterior  focus :  after  refraction  it  is 
parallel  to  the  axis. 

The  point  of  intersection  of  two  of  these  straight  lines  is  the  image. 
There  are  three  possible  constructions,  therefore,  by  which  we  may 
obtain  the  image  of  this  point. 

^ H/ 


Fig.  13.  —  Refraction  by  a  spherical  surface.     Construction  of  the  image.     C,  the  cer  tre  ;  4>1( 
the  anterior,  focns  ;  $2.  the  posterior  focus;  O,  the  object;  I,  the  image.  AS  =/lf  BS 


Fig.  13  shows  the  construction  by  means  of  rays  2°  and  3°.  The 
triangles  DA^  and  ^SG  and  the  triangles  HM<£2  and  4>2BE  being 
similar,  we  have  the  same  relation  as  for  the  mirrors 


I         -    *\    -         /, 

whence  we  deduce  the  two  general  formulae 

/!  /„  =  F,  F,  ami  A  :+  Jl  =  J. 

h  h 


OPTIC  PRINCIPLES 


13 


The  image  is  real  and  inverted  when  the  object  is  beyond  the  anterior 
focus;  it  is  smaller  than  the  object  if  the  distance  of  the  latter  from 
the  surface  is  greater  than  2F1?  larger  if  the  distance  is  less  than  zF^.  If 
the  object  is  between  the  focus  and  the  surface,  the  image  is  virtual, 
erect  and  enlarged  and  behind  the  object. 

If  the  surface  is  concave  the  radius  is  to  be  considered  negative.  The 

focal  distances  then  become  negative:  F1=--ir|n-,  F,  — J^y, 

which  indicates  that  the  anterior  focus  is  situated  behind  and  the  pos- 
terior focus  in  front  of  the  surface. 

If,  in  this  latter  case,  the  rays  pass  from  a  dense  medium  (with  index 
=  n)  into  a  rarer  medium  (with  index  =  i),  we  must  in  the  formulae 
replace  n  by  -£-  •  The  focal  distances  then  become  positive  again :  Fx  = 
•£rr,  F2  =  — ~.  This  is  what  happens  when  rays,  after  having  passed 
through  the  first  surface  of  a  biconvex  surface,  meet  the  second. 

POWER  OF  A  REFRACTING  SURFACE.  —  The  refracting  power  of  a  sur- 
face is  expressed  in  dioptrics  by  the  inverse  of  the  anterior  focal  dis- 
tance measured  in  meters:  D  =  -—  =  --^-  •  (i) 

If  for  example  the  anterior  focal  distance  is  24  millimeters  (anterior 
surface  of  the  cornea)  the  refracting  power  is  D  =  0-^  =  42  dioptrics. 


Fig.  14.  —  Refraction  by  a  parabolic  surface.     A,  luminous  point ;   F,  its   image ;   BG, 
normal;  BH,  radius  of  curvature. 

REFRACTION  BY  A  SURFACE  OF  REVOLUTION  OF  THE  SECOND  DE- 
GREE. —  If  the  luminous  point  is  on  the  axis,  refraction  at  a  given  point 

(1)  [In  other  words,  we  define  the  refractive  power  of  a  convex  surface  at  a  certain  point  B  (fig.  14) 
as  the  dioptric  power  of  an  infinitely  thin  plano-convex  lens  obtained  by  cutting  off  a  piece  of  the 
refracting  surface  by  a  plane  at  right  angles  to  the  normal  at  B  and  very  near  to  this  point.  Such  detached 
plano-convex  lens,  surrounded  by  the  first  medium,  has  a  posterior  focal  distance  F2  equal  to  the  an- 


terior focal  distance 


^  equal  to  -  -  and  a  refracting  power  =  -=-  =.  -=-  =  n 
71  —  1  r  o 


-=- 
r  i 


If  the  surface  is 


not  a  sphere  but  a  surface  of  revolution  of  the  second  degree,  we  must  replace  R  by  the  normal  N  at 
the-  point  B].—  W. 


14  PHYSIOLOGIC   OPTICS 

B  (fig.  14)  takes  place  in  the  same  manner  as  if  the  surface  was  replaced 
by  a  sphere  drawn  around  the  point  G  where  the  normal  BG  meQts  the 
axis.  If  we  designate  as  N  the  normal  BG,  the  refracting  power  of  the 

surface  at  the  point  B  is  therefore  D  =  n  ~     . 

We  can  indeed  calculate  the  focal  distances  for  a  surface  of  revolution 
exactly  as  we  have  done  for  the  sphere,  and  we  find  the  same  ex- 
pressions by  replacing  R  by  N.  It  is  well  to  note  that  it  is  the  normal 
BG  and  not  the  radius  of  curvature  BH  which  enters  into  the  formulae.  — 
These  remarks  are  of  importance  for  the  theory  of  accommodation  and 
of  keratoconus. 

14.  Infinitely  Thin  Lenses.  —  The  theory  of  lenses  is  very  simple  if  we 
can  neglect  the  thickness.  We  designate  as  axis  the  straight  line  which 
joins  the  two  centers  of  the  surfaces,  and  as  optic  center  the  point  where 
this  axis  crosses  the  lens.  This  point  enjoys  this  property  that  a  ray 
passing  through  it  crosses  the  lens  without  deviation. 

FOCAL  DISTANCE  OF  A  BICONVEX  LENS.  —  Let  us  designate  the  radii 
of  curvature  of  the  two  surfaces  as  Rj  and  R2.  Incident  parallel  rays 
which  meet  the  first  surface  are  refracted  towards  the  posterior  focus, 
the  distance  of  which,  as  we  have  seen,  is  equal  to  ^~.  This  point 
now  acts  as  the  object  for  the  second  surface;  as  it  is  behind  the  latter 
its  distance  is  to  be  considered  as  negative.  In  the  formula 


fi  is  therefore  equal  to  —  £ir?       Fx  has  the  value  of  £^\   and  F2  of 
^ri(§  13).    We  have  therefore 

n  tVo  Rn 


The  posterior  focus  of  the  lens  is  deduced,  therefore,  from  the  ex- 
pression 


OPTIC  PRINCIPLES 


15 


The  anterior  focal  distance  is  equal  to  the  posterior  focal  distance,  for 
it  is  clear  that  on  rotating  the  lens  the  expression  -p~  remains  the  same. 
We  must  replace  Rj  by  R2,  and  vice  versa,  which  does  not  change  the 
expression. 

CONSTRUCTION  OF  THE  IMAGE  (fig.  15).  —  To  construct  the  image  A' 
of  a  point  A  we  can  draw : 

i°.  The  ray  AC  passing  through  the  optic  center:  this  ray  suffers  no 
deviation ; 

2°.  The  ray  AD  parallel  to  the  axis :  after  refraction  this  ray  passes 
through  <J>2; 

3°.  The  ray  A^  passing  through  the  anterior  focus:  after  refrac- 
tion this  ray  is  parallel  to  the  axis. 


p. 


Fig.  15.  —  Construction  of  the  image  formed  by  a  thin  lens.   BC  =/lf  B'C  =/2,  C*j 


These  three  rays  intersect  at  the  point  A,  but  two  suffice  to  find  this 
point. 

The  triangles  AB^  and  S^CE  on  one  side,  and  the  triangles  DC4>2 
and  4>2B'A'  on  the  other  give  us,  as  in  the  case  of  the  mirrors,  the 
relations  : 


which  can  also  be  written 


i.i        i 

— h  -7-  =  ~ET  • 


By  the  formula  or  by  construction  we  find  the  following  relations 
between  object  and  image  : 

I.  If  the  object  is  beyond  the  focus,  the  image  is  real  and  inverted,  and 
on  the  other  side  of  the  lens.  It  is  enlarged  if  the  distance  of  the  object 
from  the  lens  is  less  than  double  the  focal  distance,  diminished  in  the 
contrary  case.  If  the  distance  of  the  object  from  the  lens  is  equal  to 
double  the  focal  distance,  the  object  and  image  are  of  the  same  size. 


10  PHYSIOLOGIC   OPTICS 

2.  If  the  object  is  between  the  focus  and  the  lens,  the  image  is  virtual, 
erect  and  enlarged;  it  is  on  the  same  side  of  the  lens  as  the  object,  but 
farther  away. 

If,  after  having  placed  a  strong  lens  on  a  printed  sheet,  we  withdraw 
it  gradually  from  the  sheet,  looking  through  it  at  some  distance  we  see 
at  first  an  erect  image  which  is  virtual  and  situated  back  of  the  lens  and 
which  increases  in  size  the  farther  we  remove  the  latter,  until  the  sheet 
is  at  the  focus;  at  that  moment  the  image  disappears  (it  becomes  so 
large  that  a  single  point  fills  the  entire  field  of  the  lens).  Withdrawing 
the  lens  still  farther  we  see  an  inverted  image  situated  between  the  lens 
and  the  eye.  It  is  enlarged  at  first,  but  rapidly  diminishes  according  as 
the  lens  is  removed. 

CONCAVE  LENSES.  —  While  biconvex  lenses  and  plano-convex  lenses, 
which  act  in  the  same  manner,  make  incident  rays  converge,  concave 
lenses  make  them  diverge.  The  formula  of  the  focal  distance  remains  the 
same,  but  as  the  surfaces  are  concave  the  radii  must  be  considered  as 
negative  : 


The  focal  distance  is  therefore  negative  also,  that  is  to  say  the  focus 
is  on  the  side  from  which  the  rays  come.  Incident  parallel  rays  continue 
their  course  as  if  they  come  from  the  focus  situated  on  the  same  side  as 
the  object. 

The  construction  of  the  image  is  analogous  to  that  which  we  have 
employed  for  biconvex  lenses.  It  gives  us  the  same  relations  as  before 
with  the  necessary  changes  of  the  signs  : 

I  /,  —  F  11  1 

and    - 


o   •  k  t\         -/, 

As  long  as  the  object  is  real,  the  image  is  virtual,  erect  and  smaller. 
It  is  at  the  focus  when  the  object  is  at  infinity.  According  as  the  latter 
approaches  the  lens,  the  image  does  likewise^1) 

MENISCI.  —  A  lens,  one  surface  of  which  is  convex  and  the  other  con- 
cave, is  called  a  meniscus.  According  as  the  radius  of  the  convex  sur- 
face or  that  of  the  concave  surface  is  smaller  the  meniscus  is  convergent 
or  divergent  (positive  or  negative).  The  positive  meniscus  is  thicker  in 
the  middle,  the  negative  is  thicker  towards  the  edges.  These  rules  are 
valid,  however,  only  when  the  thickness  is  negligible,  which  often  does 
not  happen. 

(!)  Generally  the  object  and  image  move  in  the  same  direction  in  all  cases  of  refraction,  in  an  opposite 
direction  in  cases  of  reflection. 


OPTIC  PRINCIPLES 


17 


METHODS  OF  MEASURING  THE  FOCAL  DISTANCE  OF  A  LENS.  —  The 
method  most  frequently  employed  by  oculists  consists  in  looking  at 
exterior  objects  through  the  lens,  subjecting  the  latter  to  slight  dis- 
placements. We  then  notice  that  exterior  objects  are  displaced  in  the 
same  direction  as  the  lens  if  the  latter  is  concave,  in  the  contrary  direc- 
tion if  it  is  convex.  In  other  words,  if  the  eye  is  in  front  of  the  middle 
of  the  lens  the  rays  reach  it  without  any  deviation;  but  if  the  eye  is 
placed  before  a  peripheral  part  of  the  lens  it  receives  rays  deflected  by 
reason  of  the  prismatic  effect  of  the  glass,  and  this  effect  is  greater  in 
proportion  as  the  part  through  which  the  eye  looks  approaches  the 
periphery  (fig.  16).  —  To  determine  the  focal  distance  of  a  lens  we  find 
in  the  test  case  the  glass  which  neutralizes  it  (i). 


Fig.  16. 

But  we  must  remember  that  the  numeration  of  the  glasses  in  the  test 
case  is  frequently  not  very  exact.  —  Lenses  have  the  same  curvature  on 
both  sides ;  we  have  therefore  -J-  =  2  (nB~ l  • ;  the  index  of  the  lens  is 
approximately  n=i.$,  which  means  that  the  focal  distance  and  the 
radius  are  nearly  the  same  length  (-J-  =  2  (1-5B~ 1}  =  ~). —  It  was 
customary  for  a  long  time  to  number  lenses  according  to  their  radius  of 
curvature ;  as  the  index  is  generally  a  totle  more  than  1.5,  it  would  follow 
that  the  strong  lenses  would  have  a  focal  distance  somewhat  less  than 
the  number  they  bear,  but  in  the  case  of  convex  glasses  the  error  would 
be  nearly  compensated  for  by  the  influence  of  the  thickness  of  the  glass. 

Later,  numeration  by  dioptrics  (2)  was  introduced;  and  to  obviate  the 
necessity  of  changing  the  moulds  in  which  glasses  are  ground  the  manu- 

1 i)  We  can  also  use  with  advantage  the  American  spherometer,  a  little  instrument  with  which  we 
measure  the  radius  of  curvature  and  thus  indirectly  the  refracting  power  of  the  glass. 

(2)  [In  1872  Monoyer,  of  France,  first  proposed  the  term  "dioptrie."    He  says  in  the  Annales  d'Ocu- 
listique,  Vol.  68,  page  111 :  "  C'est  le  pouroir  dioptrique  de  la  lentitte  d'un  metre  ou  100  centimetres  de  lon- 
gueur focale  qui  doit  servir  d'unite.    Cette  unite  nous  I'appellerons  unite  metrtque  ou  decimale  de  refraction 
ou  simplement— DIOPTRIE— si  Von  veut  biens  nous  permettre  ce  ntologivme  derive  conformement  aux  usages 
scientiflqucs.    This  term  has  been  adopted  all  over  the  world  and  in  English  can  have  only  one  philo- 
logically  correct  translation,  that  is  dioptry.    This  correct  form  has  been  employed,  instead  of  diopter, 
all  through  this  work  ]—W. 


18  PHYSIOLOGIC   OPTICS 

facturers  simply  wrote  the  numbers  in  dioptrics  on  such  of  the  old 
lenses  as  most  nearly  corresponded  with  such  numbers.  It  is  only  re- 
cently that  lenses  have  been  manufactured  strictly  according  to  the 
dioptric  series. 

For  all  these  reasons  it  may  be  useful  for  an  oculist  to  be  able  to  de- 
termine the  focal  distance  directly.  For  convex  lenses  we  need  only 
form  the  image  of  a  distant  object  on  a  screen.  The  distance  of  the 
lens  from  the  screen  is  the  focal  distance.  —  For  the  concave  lenses  we 
place  a  flame  at  a  great  distance  so  that  it  forms  its  virtual  image  at  the 
focus  of  the  lens  ;  we  then  place  a  screen  behind  the  latter  and  find  the 
position  to  give  to  it  in  order  that  the  luminous  circle  formed  by  the 
lens  would  have  a  diameter  equal  to  double  that  of  the  lens.  The  dis- 
tance of  the  latter  from  the  screen  is  the  equal  to  the  focal  distance. 

We  can  determine  the  radii  of  curvature  by  means  of  reflection 
images,  by  following  the  formulae  which  we  have  given  for  the  mirrors. 
Knowing  the  radii  and  focal  distance  we  can  calculate  the  index  by  the 
formula  -jr  =  (n-i>  (^-  +  -^-). 

REFRACTING  POWER  OF  A  LENS.  —  The  refracting  power  (D)  of  a  lens 
is  expressed  in  dioptrics  by  the  inverse  of  the  focal  distance  measured 
in  meters  : 


We  can  better  realize  the  meaning  of  this  expression  if  we  recall  the 
fact  that  we  expressed  the  refracting  power  of  a  surface  by  the  inverse 
of  the  anterior  focal  distance,  1jL^  .  The  refracting  power  of  an  in- 
finitely thin  lens  is,  therefore,  simply  the  sum  of  the  refracting  powers 
of  its  two  surfaces. 

The  refracting  power  of  an  optical  system  composed  of  several  in- 
finitely thin  lenses  placed  very  ne,  .  one  another  is  equal  to  the  sum  of 
the  powers  of  the  lenses. 

15.  Theory  of  Gauss.  —  If  the  lenses  are  not  so  thin  that  their  thick- 
ness can  be  neglected,  nor  placed  so  near  one  another  that  we  can  neg- 
lect their  distances,  we  can  find  the  position  and  size  of  the  image  by 
construction  or  by  calculation  by  the  rules  which  we  have  given  for  re- 
fraction by  spherical  surfaces  :  we  construct  or  calculate  in  the  first 
place  the  image  formed  by  the  first  surface;  this  image  then  serves  as 
the  object  for  the  second  surface  and  so  forth.  But  it  is  much  simpler 
to  use  the  theory  of  Gauss.  We  will  briefly  explain  the  essential  points 
of  this  theory,  which  is  applicable  to  every  optical  system  composed  of 


OPTIC  PRINCIPLES  19 

spherical  surfaces,  supposing  that  the  system  be  centered,  that  is  to  say 
that  all  the  centers  of  the  surfaces  are  on  the  axis  and  that  the  aperture 
of  the  surfaces  is  small. 

According  to  the  theory  of  Gauss,  every  optic  system  has  six  cardinal 
points,  namely : 

Two  principal  points,  1^,  h2  (fig.  17) ; 

Two  nodal  points,  Kx,  K2; 

One  anterior  focus,  ^  ; 

One  posterior  focus,  <J>2. 

The  anterior  focal  distance,  F1  =  ^  hlt  is  the  distance  of  the  anterior 
focus  from  the  first  principal  point ;  it  is  equal  to  the  distance  of  the 
second  nodal  point  from  the  posterior  focus,  K2  3>2- 

The  posterior  focal  distance,  F2  —  h2  <K,  is  the  distance  of  the  second 
principal  point  from  the  posterior  focus;  it  is  equal  to  the  distance  of 
the  anterior  focus  from  the  first  nodal  point,  ^  K±. 


Fig.  17. 

It  follows  that  the  distance  of  the  first  principal  point  from  the  first 
nodal  point  is  equal  to  the  distance  of  the  second  principal  point  from 
the  second  nodal  point  and  to  the  difference  between  the  focal  distances 
F2  —  Fx.  The  distance  between  the  two  principal  points  is  equal  to  the 
distance  between  the  two  nodal  points. 

The  ratio  between  the  focal  distances  is  equal  to  the  ratio  between 
the  indices  of  the  first  and  last  medium  Jra  =  n. 

We  call  principal  planes  two  planes  perpendicular  to  the  axis  and  pass- 
ing through  the  two  principal  points.  The  image  of  an  object  situated 
in  the  first  principal  plane  is  formed  in  the  second  principal  plane  and 
vice  versa.  It  is  the  same  size  as  the  object  and  its  direction  is  the  same 
as  that  of  the  object. 

A  ray  which,  in  the  first  medium,  passes  through  the  first  nodal  point, 
passes,  after  refraction,  through  the  second  nodal  point,  and  the  direc- 
tions of  the  ray  before  and  after  refraction  are  parallel. 


20 


PHYSIOLOGIC   OPTICS 


Knowing  the  position  of  the  cardinal  points,  the  image  of  a  given  point 
can  be  found  by  construction  or  calculation  in  a  manner  analogous  to 
that  which  we  have  already  employed  in  the  case  of  infinitely  thin  lenses. 
To  find  the  image  of  the  point  G  (fig.  18)  by  construction  we  can  choose 
two  of  the  three  following  rays : 

i°.  The  ray  GA,  which  is  parallel  to  the  axis,  must  cut  the  second 
principal  plane  at  D,  at  a  distance  from  the  axis  equal  to  Ahit  and  it  must 
pass  through  4>2.  Its  direction  is  therefore  DH. 

2°.  The  ray  GB,  which  passes  through  the  anterior  focus  4>15  must, 
after  refraction,  be  parallel  to  the  axis :  It  will  then  take  the  direction 
EH. 


Fig.  18.  —  Construction  of  the  image  I  of  the  object  O.   L*^  =  /x.  4^  ht  =  Flt  L/^  =fl 
M*2  =  I,,  *,  h,  =  F2,  Mft,  =/, 

3°.  The  ray  GK15  directed  towards  the  first  nodal  point,  takes,  after 
refraction,  the  direction  K2  H,  parallel  to  its  first  direction. 

The  triangles  GL^  and  Eh^^  on  one  side  and  the  triangles  D/L>4>2 
and  HM4>2  on  the  other  give  the  relation 


We  have,  therefore,  as  before  l^  /2  =  Fx  F2,  and  we  can  deduce  the 
other  general  formula  -^-  +  ~jj-  =  I.  —  Note  that  /t  is  reckoned  as  F± 
from  the-  first  principal  point,  f2  on  the  contrary  from  the  second  prin- 
cipal point. 

METHODS  OF  FINDING  THE  CARDINAL  POINTS  OF  A  GIVEN  SYSTEM.  — 
a.  CONSTRUCTION  (fig.  19).  —  We  draw  an  incident  ray  parallel  to  the 
axis  and  we  construct  its  course  by  the  law  of  Descartes  or  by  the  for- 
mulae which  we  have  given  for  refraction  by  spherical  surfaces.  We 
thus  find  the  posterior  focus.  We  then  prolong  the  incident  and  emerg- 
ent rays;  their  point  of  intersection  is  situated  in  the  second  principal 
plane,  and  the  perpendicular  let  fall  from  this  point  on  the  axis  marks 


OPTIC  PRINCIPLES 


21 


the  second  principal  point  h2.     Repeating  the  same  construction  with 
a  ray  parallel  to    the  axis,  coming  from  the  other  side,  we  find  in  the 


Fig.  19.  —  Construction  to  find  the  second  principal  plane. 
» 

same  manner  the  anterior  focus  and  the  first  principal  point.  Knowing 
these  four  points  we  can  deduce  the  position  of  the  nodal  points,  since 
the  distance  of  the  first  nodal  point  from  the  anterior  focus  is  equal  to 
the  distance  of  the  second  principal  point  from  the  posterior  focus,  etc. 
b.  CALCULATION.  —  Let  us  designate  by  A  and  B  the  two  optic  sys- 
tems which  we  wish  to  combine,  their  focal  distances  by  F\  and  F'2  (for 
the  system  A)  and  by  F'^  and  F"2  (for  the  system  B),  and  the  distance 
of  the  posterior  focus  of  the  system  A  behind  the  anterior  focus  of  the 
system  B,  by  d.  We  can  then  find  the  cardinal  points  of  the  combined 
system  by  means  of  the  following  formulae  in  which  y±  indicates  the  dis- 
tance of  the  anterior  focus  of  the  combined  system  behind  the  anterior 
focus  of  the  system  A,  and  y2  the  distance  of  the  posterior  focus  of  the 
combined  system  in  front  of  the  posterior  focus  of  the  system  B. 


.    F',F", 
d 


The  deduction  of  these  formulae  offers  no  difficulties.  An  incident 
ray,  parallel  to  the  axis,  will  pass  after  refraction  by  the  system  A, 
through  its  posterior  focus,  and,  after  refraction  by  the  system  B, 
through  the  point  4>  (fig.  190) ;  the  posterior  focus  of  the  compound  sys- 
tem. Its  prolongation  meets  the  prolongation  of  the  incident  ray  at  D 


22 


PHYSIOLOGIC   OPTICS 


so  that  h2  is  the  second  principal  plane  of  the  compound  system.    After 
the  formula  of  Newton  we  have 


2/2    = 


_  F'^F", 


On  the  other  hand  the  figure  gives  us  the  relations : 

a  F'2  F2  F',  (y,  +  F"J 

T'-d  +  F",   -y2  +  F",   °r  F»-       -  d  +  F",    ' 


F' 


(d  +  F"! 


_    F',  F", 


We  find  the  value  of  yx  and  Fx  by  supposing  the  light  to  come  from 
the  other  side.  Knowing  thus  the  focal  distance  and  the  position  of 
the  foci  it  is  easy  to  calculate  those  of  the  other  cardinal  points. 


4 
/^ 


/' 


^ 


-Z) 


19a. 

In  the  case  which  the  figure  represents,  d  is  negative,  since  the  pos- 
terior focus  of  A  is  situated  in  front  of  the  anterior  focus  of  B  ;  F!  and  F2 
are,  therefore,  also  negative,  as  well  as  y^  and  y2 ;  the  compound  system 
acts  as  a  concave  lens.  If  d  —  0  the  focal  distances  are  infinity :  incident 
parallel  rays  are  again  parallel  after  refraction.  Such  a  system  is  called 
telescopic;  a  telescope  focused  on  infinity  by  an  emmetropic  observer  is 
an  illustration  of  it.  The  distance  d,  the  sign  of  which  determines  the 
character  of  the  compound  system  is  often  called  the  interval;  in  the 
cases  which  interest  us  it  is  nearly  always  positive. 


OPTIC  PRINCIPLES 


23 


SPECIAL  CASES.  —  As  the  focal  distances  are  proportional  to  the  in- 
dices of  the  first  and  last  media,  they  ought  to  be  equal  if  the  first  and 
last  media  are  identical,  which  is  true  for  nearly  all  optical  instruments. 
In  this  case  the  distance  of  the  anterior  focus  from  the  first  principal 
point  is  equal  to  its  distance  from  the  first  nodal  point,  that  is  to  say 
the  first  principal  point  coincides  with  the  first  nodal  point  and  the  sec- 
ond principal  point  with  the  second  nodal  point. 

This  is  what  occurs  in  the  case  of  thick  lenses,  in  which  case  we  can 
find  the  nodal  points  by  a  simple  construction.  Let  Q  (fig.  20)  be  the 
center  of  the  first  surface ;  C2  that  of  the  second ;  C2  A  any  radius  what- 
ever of  the  second  surface,  and  Q  B  a  radius  of  the  first  surface  parallel 
to  C2  A.  Let  us  draw  the  straight  line  AB,  which  represents  the  course 
of  a  ray  in  the  interior  of  the  lens;  DB  and  AE  indicate  its  direction 
outside  the  lens.  It  is  easy  to  see  that  these  two  straight  lines  are 
parallel;  the  angles  i  are,  in  fact,  equal,  since  the  angles  r  are  equal. 

Prolonging  DB  and  AE  they 
cut  the  axis  at  the  two  points 
K!  and  K2,  which  are  the  two 
nodal  points.  The  point  O  is 
the  optic  center  of  the  lens. 
It  is  the  image  of  Kx  in  rela- 
tion to  the  first  surface,  and 
that  of  K2  in  relation  to  the 
second  surface. 

In  an  infinitely  thin  lens,  the 
nodal  points  and  the  principal 
points  all  coincide  with  the 
optic  center.  If  the  entire 
system  is  represented  by  a 
simple  refracting  surface,  both 

Fig.  20.  —  Construction  to  find  the  nodal  points    principal  points   coincide  with 
of  a  thick  lens.  ,«  . 


points  with  the  center. 

The  mirrors  may  be  considered  as  dioptric  systems,  in  which  the  last 
medium  has  an  index  equal  to  that  of  the  first  medium,  but  with  the 
contrary  sign,  since  the  rays  run  in  a  contrary  direction.  The  two 
principal  points  coincide  with  the  surface,  the  nodal  points  with  the 
center,  and  the  focus  is  at  an  equal  distance  between  the  two  (since 
F!  =  —  F2).  The  compound  reflecting  systems  likewise  have  only  one 
principal  point  and  one  nodal  point,  and  the  focus  is  situated  at  an  equal 


24  PHYSIOLOGIC  OPTICS 

distance  between  them.  Such,  for  example,  is  the  case  in  the  compound 
systems  which  give  rise  to  the  images  of  Purkinje  in  the  eye. 

EXAMPLE  i.  —  To  find  the  cardinal  points  of  the  crystalline  lens. 

Suppose  the  crystalline  lens  has  a  thickness  of  4  millimeters,  that  the 
radius  of  the  anterior  surface  is  10  millimeters  and  that  of  the  posterior 
surface  6  millimeters.  Let  us  take  1.33  as  the  index  of  the  aqueous 
humor  and  the  vitreous  body,  and  suppose  that  the  index  of  the  crystal- 
line lens  in  relation  to  these  liquids  is  about  1.06. 

In  this  case  each  of  the  systems  A  and  B  is  represented  by  a  single 
refracting  surface.  The  focal  distances  of  the  system  A  are: 

R  10 


n  —  1  ~"  0.06 


_          ,  10  X  1.06   __  177 

2  ~~      —  1  ~  0.06 


those  of  the  system  B  are  : 


1.06 


l.Oti 

The  interval  d  is  the  distance  of  the  posterior  focus  of  the  system  A 
from  the  anterior  focus  of  the  system  B;  the  former  is  situated  at  177 
millimeters  behind  the  anterior  surface,  the  latter  at  106  millimeters  in 
front  of  the  posterior  surface  ;  the  thickness  of  the  crystalline  lens  being 
4  millimeters,  we  will  have  ^=177  miljimeters  +  106  millimeters  —  4 
millimeters  =  279  millimeters,  and 


_  F"x  F",  _  106X100  _ 
~~^~  279 

167  X  106 


279 


=  63.4™ 


The  anterior  focus  of  the  crystalline  lens  being  situated  at  106  milli- 
meters behind  the  anterior  focus  of  the  first  surface  C,  which  is  at  167 


OPTIC  PRINCIPLES  25 

millimeters,  its  distance  as  far  as  that  surface  will  be  167 —  106  =  61  mil- 
limeters, and  as  the  focal  distance  is  63.4  millimeters,  the  first  principal 
point  of  the  crystalline  lens  will  be  placed  at  2.4  millimeters  behind  the 
anterior  surface.  The  second  principal  point  will  be  situated  at  an  equal 
distance,  at  100  —  38  — 63.4  =  —  1.4  millimeters,  that  is  to  say,  1.4  mil- 
limeters in  front  of  the  posterior  surface. 

Both  focal  distances  are  equal,  as  they  must  be,  since  the  surrounding 
media  are  alike.  The  refracting  power  of  the  crystalline  lens  would  be 
with  these  data  6-3^  =  15.8  D. 

EXAMPLE  2.  —  Let  us  consider  the  cornea  as  a  simple  refracting  sur- 
face with  a  radius  of  8  millimeters  surrounded  in  front  by  air  (n  =  i), 
behind  by  the  aqueous  humor  (n  =  1.33  =  f ).  The  distance  of  the 
anterior  surface  of  the  cornea  from  the  anterior  surface  of  the  crystalline 
lens  is  3.6  millimeters.  To  combine  the  cornea  with  the  crystalline  lens  the 
cardinal  points  of  which  we  have  just  found. 

Here  the  cornea  forms  the  sstem  A.    Its  focal  distances  are : 


*-.-**-«- 

The  principal  points  coincide  with  the  surface.  The  focal  distances 
of  the  system  B  are  those  found  above  for  the  crystalline  lens. 

The  interval  d  is  the  distance  of  the  anterior  focus  of  the  crystalline 
lens  as  far  as  the  posterior  focus  of  the  cornea:  d  =  6i  mm.  +  32 
mm.  —  3.6  mm.  =  89.4.  With  these  data  we  find  for  the  entire  optic 
system  of  the  eye : 

24  X  32 


89.4 


=  8.6mi 


The  following  table  gives  a  general  idea  of  such  an  optic  system. 
By  position  of  a  point  we  mean  the  distance  of  that  point  behind  the  sum- 
mit of  the  cornea. 


26  PHYSIOLOGIC  OPTICS 

Simplified  Eye. 

Index  of  aqueous  humor  and  vitreous  body 1.33 

—  the  crystalline  lens 1.41 

Radius  of  curvature  of  the  cornea 8mm 

—  anterior  surface  of  the  crystalline  lens. .  10mm 

—  posterior  surface  of  the  crystalline  lens . .       6mm 

Depth  of  the  anterior  chamber 3.6mm 

Thickness  of  the  crystalline  lens 4mm 

Anterior  focal  distance  of  the  cornea 24mm 

Posterior  focal  distance  of  the  cornea 32mm 

Focal  distance  of  the  crystalline  lens 63.4mm 

Position  of  the  anterior  principal  point  of  the  crystalline  lens 6mm 

—  —      posterior  principal  point  of  the  crystalline  lens 6.2mm 

Anterior  focal  distance  of  the  eye  17mm 

Posterior  focal  distance  of  the  eye 22.7mm 

Position  of  the  anterior  principal  point  of  the  eye 1.6mm 

—  —      posterior  principal  point  of  the  eye 1.9mm 

—  —      anterior  nodal  point  of  the  eye 7.3mm 

—  —      posterior  nodal  point  of  the  eye 7.6mm 

—  —      anterior  focus  of  the  eye —  15.4mm 

—  —      posterior  focus  of  the  eye 24.6mm 

Kefracting  power  of  the  cornea 42  D. 

—      crystalline  lens 16  D. 

—        —     eye 59  D. 

We  shall  see  in  the  following  chapter  that  the  data  with  which  we 
have  made  these  calculations  are  not  rigorously  exact;  nevertheless, 
they  give  a  very  close  approximation,  generally  sufficient  for  our  pur- 
pose. Later  I  shall  have  recourse  more  than  once  to  this  system,  which 
I  call  the  simplified  eye,  to  distinguish  it  from  the  complete  optic  system 
of  which  we  shall  treat  in  the  following  chapter. 

Bibliography.  —  Complete  development  of  the  system  of  Gams  in  the  introduction  to 
the  physiologic  optics  of  Helmholtz. 

Among  the  numerous  treatises  on  geometric  optics,  I  shall  cite: 

Jamin  and  Bouty.  Cours  de  physique  de  I'Ecole  Polytechnique,  1886.  —  Pouillet-Muller. 
Lehrbuch  der  Physik  und  Meteorologie,  8th  edition.  Braunschweig,  1872.  Of  an  easy  study. 
—  Wiillner  (Ad.).  Lehrbuch  der  ExDerimentalphysik.  II.  Leipzig,  1877.  —  Lorenz  (L.).  Die 
Lehre  vom  Licht.  Leipzig,  1877. 

Among  the  more  complete  works,  but  of  a  more  difficult  study,  we  shall  cite : 

Verdet  (E.).  (Euvres.  Paris,  1872.  —  Herschel  (Sir  J.  F.  W.).  Light.  London.  1845. 
In  French  by  Verhulst  (P.  F.)  and  Quetelet  (A.).  Paris,  1829.  —  Heath  (K.  S.).  A  Treatise 
on  Geometric  Optics.  Cambridge,  1877.  —  Gariel  (G.  H.).  Etudes  d'optique  geometrique.  Paris, 
1889. 

The  beautiful  works  of  E.  Abbe  resulted  in  considerable  progress  in  geometric  optics  dur- 
ing the  last  twenty  years.  We  will  find  an  account  of  them  in  Czapski  (S. ),  Theorie  der 
optischen  Instrumente,  Breslau,  1893,  and,  in  a  more  easily  accessible  form,  in  the  new  edition 
of  Pouillet-Muller,  by  Pfaundler  (L.)  and  Luoamer  (O.),  Braunschweig,  1897. 


CHAPTER  II. 

THE  OPTIC  SYSTEM  OF  THE  EYE. 


16.  Optic  Constants  of  the  Eye.  —  By  means  of  the  theory  of  Gauss  we 
can  calculate  the  cardinal  points  of  any  optic  system  if  we  know  the 
position  and  curvature  of  the  surfaces  and  the  index  of  the  media.  To 
calculate  the  optic  system  of  the  eye  we  must  know,  therefore,  as  ex- 


Fig.  21.  — The  optic  system  of  the  eye  (left),  C1?  C2,  C3,  C4,  the  centers  of  the  four  surfaces 
in  their  natural  order;  AB,  optic  axis  ;  L,  visual  line. 

actly  as  possible  those  numbers  which  are  frequently  called  the  optic 
constants  of  the  eye.  Those  which  I  have  given  in  the  examples  in  the 
preceding  chapter  are  only  approximate.  The  following  table  gives 
the  constants  of  an  eye,  which  I  have  measured  as  carefully  as  possible 
(fig.  21): 

Optic  Constants  of  the  Eye. 

Position  of  the  anterior  surface  of  the  cornea 0 

—  posterior  surface  of  the  cornea 1.15mm 

—  anterior  surface  of  the  crystalline  lens 3.54mm 

—  posterior  surface  of  the  crybtalline  lens 7.60mm 

Radius  of  the  anterior  surface  of  the  cornea 7.98mra 

—  —     posterior  surface  of  the  cornea 6.22mm 

—  —      anterior  surface  of  the  crystalline  lens 10.20mm 

—  —      posterior  surface  of  the  crystalline  lens 6.17mm 

27 


28  PHYSIOLOGIC   OPTICS 


Index  of  the  air 

—  —      cornea 

—  —      aqueous  humor 
Total  index  of  the  crystalline  lens, 
Index  of  the  vitreous  body 


accepted 


1 

1.377 

1.3365 

1.42 

1.3365 


The  positions  and  radii  of  the  surfaces  as  stated  are  according  to 
measurements  which  I  made  by  methods  which  I  shall  mention  later. 

The  only  difference  of  any  importance  between  them  and  those  found 
up  to  the  present  arises  from  the  thickness  of  the  crystalline  lens  which, 
in  his  schematic  eye  Helmholtz  put  down  as  3.6  millimeters,  certainly  too 
small  a  number  to  be  considered  an  average.  I  have  also  added  the 
numbers  for  the  posterior  surface  of  the  cornea  which  I  was  the  first  to 
measure. 

As  to  the  indices  which  cannot  be  measured  directly  on  the  living  eye 
I  have  put  down  1.377  for  the  cornea  after  a  measurement  of  Matthiessen, 
which  I  also  have  verified.  Those  of  the  aqueous  humor  and  vitreous 
body  are  very  exactly  known ;  we  can,  indeed,  determine  them  with 
great  exactness  by  means  of  the  refractometer  of  Abbe,  or  by  other 
analogous  methods. 

Less  is  known  of  the  index  of  the  crystalline  lens  than  of  the  other 
optic  constants  of  the  eye.  It  must  be  noted  in  the  first  place  that  this 
body  is  not  homogeneous;  its  index  gradu- 
ally diminishes  starting  from  the  center  of 
the  nucleus  towards  the  periphery.  The 
curvature  of  its  layers  diminishes  also 
towards  the  periphery,  so  that  each  layer 
takes  the  form  of  a  meniscus,  the  concavity 
of  which  is  greater  than  the  convexity.  This 
conclusion  follows  as  well  from  anatomical 
researches  as  from  optic  observations  which 
I  made  on  the  eye  of  an  ox  after  death  (i). 

There  is,  indeed,  frequently  produced,  in  the  Fie-  22-  ~  °Ptic  gystem  °f  tlie 

eye  of  an  ox  (twice  enlarged), 
crystalline  lens,  after  death,  a  differentiation 

between  the  cortical  masses  and  the  nucleus,  probably  caused  by  the  im- 
bibition of  water  by  the  superficial  parts.  In  consequence  of  this  process 


(1)  The  optic  constants  of  such  an  eye  are  as  follows  (fig.  22) : 

Radius  of  the  cornea 15  millimeters 

Position  of  the  anterior  surface  of  the  crystalline  lens 6        — 

—      posterior  surface  of  the  crystalline  lens 17         — 

Radius  of  the  anterior  surface  of  the  crystalline  lens 14 

posterior  surface  of  the  crystalline  lens 8 

anterior  surface  of  the  nucleus 8.5      — 

—        —     posterior  surface  of  the  nucleus 7         — 


THE  OPTIC  SYSTEM  OF  THE  EYE 


29 


there  is  produced  on  the  surfaces  of  the  nucleus  quite  a  regular  reflec- 
tion, so  that  instead  of  two  reflection  images  we  see  four  (fig.  23),  when 


Fig-  23.  —  Images  of  Purkinje  of  the  eye  of  an  ox  (dead).  (Flame  of  a  candle.) 
a,  image  of  the  cornea ;  6,  image  of  the  anterior  surface  of  the  crystalline  lens;  c,  image 
of  the  anterior  surface  of  the  nucleus;  d,  image  of  the  posterior  surface  of  the  nucleus;  «, 
image  of  the  posterior  surface  of  the  crystalline  lens. 

the  crystalline  lens  is  exposed  to  the  light  of  a  flame.    Now,  the  position 
of  these  images  indicates  that  the  curvature  of  the   surfaces   of  the 


A  B 

Fig.  24. —  Double  crystalline   images  in  cases  of  "false    lenticonus."     After  Demicheri. 

A.  Looking  straight  in  front. 

a,  image  of  the  cornea ;  6,  image  of  the  anterior  surface  of  the  crystalline  lens ;  c, 
image  of  the  anterior  surface  of  the  nucleus;  d,  image  of  the  posterior  surface  of  the  crys- 
talline lens,  which  coincides,  for  this  direction  of  the  look,  with  that  of  the  posterior  surface 
of  nucleus. 

B.  Looking  outwards. 

a,  image  of  the  cornea ;  b,  image  of  the  posterior  surrace  of  the  crystalline  lens;  c,  im- 
age of  the  posterior  surface  of  the  nucleus. 


30  PHYSIOLOGIC   OPTICS 

nucleus  is  considerably  greater  than  that  of  the  crystalline  surfaces. 
Dr.  Dcmicheri  has  recently  described  cases  of  alterations  of  the  human 
crystalline  lens  in  which  we  can  also  observe  four  crystalline  images ; 
their  position  also  indicates  a  greater  curvature  of  the  surfaces  of  the 
nucleus  (fig.  24). 

It  has  long  been  known  that,  as  a  result  of  this  peculiar  construction 
of  the  crystalline  lens,  its  total  index,  that  is  to  say,  the  index  of  an  imag- 
inary lens  having  the  same  form  and  the  same  focal  distance  as  the 
crystalline  lens,  is  greater,  not  only  than  the  mean  index  of  the  crystal- 
line layers,  but  even  than  that  of  the  nucleus. 

To  account  for  this  paradoxical  phenomenon,  we  may  suppose  the  crys- 
talline lens  divided  into  two  parts,  the  nucleus  and  the 
cortical  part,  supposing  the  index  uniform  in  each  part, 
but  greater  for  the  nucleus.  On  account  of  its  great 
curvature  and  high  index,  the  nucleus  (a,  fig.  25)  would 
then  have  a  very  considerable  refracting  power,  which, 
however,  would  be  diminished  by  the  influence  of  the 
cortical  layers  which  act  as  two  concave  lenses  (b,  b). 
It  is  clear  that  if  the  index  of  these  layers  were  higher 
their  influence  would  be  greater,  and  the  refracting 

power  of  the  whole  crystalline  lens  would  consequently 

1  Fig.  25. 

be  weaker. 

Thomas  Young  placed  the  index  of  the  center  of  the  nucleus  at  1.412, 
and  by  calculation  therefrom  he  deduced  1.436  for  the  total  index.  Later 
Listing  gave  1.455  f°r  the  total  index,  a  number  adopted  by  Helmholts,  but 
which  is  decidedly  too  high.  For  his  new  schematic  eye  this  latter  author 
later  adopted  an  index  (1.4371)  which  was  nearly  identical  with  that  of 
Young.  More  recently  Matthiessen  tried  to  determine  the  law  after  which 
the  index  of  the  crystalline  lens  varies  from  the  center  towards  the 
periphery,  and  to  calculate  from  it  the  total  index.  According  to  him 
the  difference  between  the  total  index  and  that  of  the  superficial  layers 
would  be  double  the  difference  between  the  index  of  the  nucleus  and 
that  of  these  cortical  layers.  He  has  found  1.437  as  the  total  index,  and 
the  average  of  his  measurements  of  the  central  index  approaches  very 
close  to  the  figures  of  Young.  —  Measurements  which  I  have  taken  after 
a  new  method,  in  collaboration  with  Dr.  Stadfeldt  (i),  seem,  however, 
to  show  that  the  law  of  Matthiessen  can  be  considered  only  as  an  approx- 
imation, and,  on  the  other  hand,  the  observations  of  those  who  have 

(1)  According  to  the  measurements  of  Stndfddt,  which  I  shall  mention  later  on,  the  mean  index  of 
the  crystalline  lens  would  be  1.435,  and  the  refracting  power  of  the  crystalline  lens  would  be  on  an 
average  19  D.  (varying  between  17  D.  and  24  D.). 


THE  OPTIC  SYSTEM  OF  THE  EYE  31 

operated  on  cataract  seem,  as  we  shall  see  later,  to  call  for  a  lower 
total  index.  Awaiting  the  result  of  new  measurements  I  adopt  the 
number  1.42. 

Thanks  to  the  special  structure  of  this  organ  the  refracting  power 
of  the  crystalline  lens  is  some  dioptrics  stronger  than  it  would  have 
been  if  its  index  had  been  uniformly  equal  to  that  of  the  nucleus.  In 
comparison  with  the  total  refraction  of  the  eye  the  increase  is  not  con- 
siderable ;  it  might  easily  have  been  obtained  by  a  slightly  greater  curva- 
ture of  one  of  the  surfaces.  The  teleologic  reason  for  this  structure  is 
rather  to  be  sought  in  the  mechanism  of  accommodation.  For,  this 
mechanism  would  be,  as  I  understand  it,  impossible  without  the  two 
peculiarities  which  characterize  the  structure  of  the  crystalline  lens :  the 
increase  of  density  and  the  increase  of  curvature  of  the  layers  according 
as  we  approach  the  center.  —  Another  advantage  of  this  structure  of 
the  crystalline  lens  consists  in  making  weaker  the  images  of  the  eye 
which  I  call  harmful  (miisibles),  and  which  I  shall  mention  farther  on. 

17.  Optic  System  of  the  Eye.  —  Applying  the  theory  of  Gauss  to  the 
data  which  we  have  just  stated,  we  find  the  following  results: 

A.  —  Optic  System  of  the  Cornea. 
Position  of  the  first  principal  point —  0.13mm 

—  —      second  principal  point —  0.14mm 

—  first  nodal  point 8.08mm 

—  second  nodal  point 8.07mm 

anterior  focus 24.53mm 

—  posterior  focus 32.47mm 

Anterior  focal  distance 24.40mm 

Posterior  focal  distance 32.61mm 

Refracting  power 40.98  D. 

B.  —  Optic  System  of  the  Crystalline  Lens. 

Position  of  the  first  nodal  point 5.96mm 

—      second  nodal  point 6.14mm 

Focal  distance  of  the  crystalline  lens 62.46mm 

Refracting  power 16.01  D. 

Combining  these  two  systems,  we  find  the  complete  optic  system  of 
the  eye. 

C.  —  Complete  Optic  System  of  the  Eye. 

Position  of  the  first  principal  point 1.54mm 

—  —      second  principal  point .  1.86mm 

—  —      first  nodal  point 7.30mm 

—  second  nodal  point 7.62mm 

—  —       anterior  focus —  15.59mm 

—  —      posterior  focus 24.75mm 

Anterior  focal  distance 17.1 3mm 

Posterior  focal  distance 22  89mm 

Refracting  power : 58.38  D. 


32 


PHYSIOLOGIC   OPTICS 


Thanks  to  these  data  we  may  eliminate,  so  to  speak,  the  entire  real 
optic  system  of  the  eye. 
In  the  system  which  we 
have  just  calculated  we 
take  into  consideration 
only  the  course  of  the 
rays  in  the  air  before  en- 
tering the  eye,  and  their 
course  in  the  vitreous 
body  after  emergence  from 
the  crystalline  lens;  their 
course  between  the  an- 
terior surface  of  the  cornea 
and  the  posterior  surface 
of  the  crystalline  lens  re- 
mains unknown  to  us. 


Fig.  26.  —  Position  of  the  cardinal  points  of  the  human 

eye  (magnified  four  times). 
A!  h2j  principal  planes ;  Kl  K2,  nodal  points. 


We  note  that  the  refracting  power  of  the  cornea  is  2.5  times  greater 
than  that  of  the  crystalline  lens.  The  sum  of  their  refracting  power  is 
not  far  from  being  equal  to  the  refracting  power  of  the  eye,  because  the 
nodal  points  of  the  cornea  are  quite  near  those  of  the  crystalline  lens  (i). 

The  following  little  table  shows  the  refracting  power  of  each  of  the 
surfaces : 

Anterior  surface  of  the  cornea -f-  47.24  D. 

Posterior  surface  of  the  cornea —    4.73  D. 

Anterior  surface  of  the  crystalline  lens +     6.13  D. 

Posterior  surface  of  the  crystalline  lens 4-     9.53  D. 

Total -j-  58.17  D. 

The  posterior  surface  of  the  cornea  has,  up  to  the  present,  been  neg- 
lected by  authors ;  we  see  that  it  has  a  certain  importance.  Its  value  is 
negative  and  almost  as  great  as  that  of  the  anterior  surface  of  the  crys- 
talline lens.  We  shall  see  that  it  seems  to  play  a  part  in  certain  forms 
of  astigmatism. 

Nevertheless,  we  commit  only  a  very  small  error  by  neglecting  it, 

(1)  The  refractipg  power  of  the  eye  would  be  exactly  equal  to  the  sum  of  the  powers  of  its  compo- 
nent systems,  if  the  anterior  principal  point  of  the  crystalline  lens  coincided  with  the  posterior  nodal 
point  of  the  cornea,  or  if  we  consider  the  cornea  as  a  single  refracting  surface,  with  its  center.  In  the 
formula  of  paragraph  15  (page  22) 

_F/ijwi 

1  ~         d 

we  would  have,  indeed,  in  this  case  d  —  FI'  +  FI",  which  gives 

111 


THE  OPTIC  SYSTEM  OF  THE  EYE  33 

that  is  to  say,  by  supposing  that  the  substance  of  the  cornea  does  not 
exist;  the  anterior  surface  simply  separating  the  air  from  the  aqueous 
humor.  By  eliminating  the  negative  influence  of  the  posterior  surface, 
the  total  refraction  of  the  cornea  should  increase,  but  the  power  of  the 
anterior  surface  diminishes  nearly  as  much,  since  we  replace  the  index 
of  the  cornea  by  the  weaker  index  of  the  aqueous  humor.  In  our  case 
we  would,  by  thus  simplifying  the  matter,  have  found  a  refracting  power 
of  the  cornea  equal  to  42.16  D.  instead  of  40.98  D.,  that  is  to  say,  we 
would  have  committed  an  error  of  1.18  D.  or  about  1/50  of  the  total 
power  of  the  eye. 

The  right  eye,  the  optic  system  of  which  I  have  calculated  (in  the  hori- 
zontal meridian),  is  the  only  one  of  which  up  to  the  present  time  we  pos- 
sess complete  measurements.  It  is  important  to  note  that  it  is  not  to 
be  considered  as  an  average.  The  radius  of  the  cornea  is  two  or  three- 
tenths  of  a  millimeter  above  the  average,  and  the  length  of  the  axis  of 
the  supposed  emmetropic  eye,  which  we  have  found  equal  to  24.75  mm., 
is  probably  also  a  little  above  the  average.  This  eye  is,  therefore,  to  be 
considered  relatively  large,  the  more  so  as  the  person  to  whom  it  belongs 
is  pretty  tall  in  stature.  A  light  degree  of  astigmatism  with  the  rule 
would  also  act  in  the  same  way.  I  have  measured  some  other  eyes,  but 
not  a  sufficient  number  to  be  able  to  establish  an  average. 

The  figures  which  I  have  just  given  apply  only  to  the  eye  of  the 
adult.  The  eye  of  the  new-born  child  is  much  smaller  (the  axis  meas- 
ures about  17  mm.  instead  of  24  mm.),  so  that  we  might  expect  to  see 
the  curvature  of  all  the  surfaces  increased  in  the  same  proportion.  This 
is  not  so :  according  to  the  concordant  measurements  of  AxenfeUl  and 
Holth  the  cornea  of  the  new-born  child  differs  but  little  from  the  adult 
cornea.  This  latter  varies  as  we  shall  see  between  quite  wide  limits 
(40  to  47  dioptrics)  and  the  values  which  we  find  in  the  new-born  child 
are  near  the  higher  limit. 

Compensation  for  the  diminution  of  the  axis  is  made  by  the  crystalline 
lens.  According  to  the  measurements  of  Stadfeldt  the  crystalline  lens 
of  the  new-born  child  is  as  thick  as  that  of  the  adult,  but  the  diameter 
is  6  mm.  instead  of  8  or  9  mm.,  whence  it  follows  that  the  curvature  of 
the  surfaces  is  very  great.  Following  are  some  figures  according  to 
Stadfeldt:. 

Radius  Radius 

Ant.  surface.  Post,  surface.  Thickness.         Diameter. 

Adult 1  lmm                6mm  3.6mm 

New-born 4.5mm            4ram  3  9mm               6mm 


34  PHYSIOLOGIC  OPTICS 

Supposing  that  the  index  is  the  same  as  in  the  adult,  the  crystalline 
lens  of  the  new-born  child  would,  therefore,  be  nearly  twice  more  re- 
fracting, and  the  crystalline  refraction  in  the  latter  would  not  be  very 
far  from  being  equal  to  the  corneal  refraction. 

18.  Aperture  of  the  System.  —  The  theory  of  Gauss  supposes  that  the 
aperture  of  the  system  is  very  small,  which  is  by  no  means  the  case  in 
the  eye,  and  many  errors  committed  in  questions  of  ocular  refraction 
seem  to  me  due  to  the  fact  that  we  do  not  sufficiently  take  into  account 
the  large  aperture  of  the  system.  In  optic  instruments  an  aperture  over 
ten  or  twelve  degrees  is  scarcely  accepted.  Supposing  that  the  pupil 
has  a  diameter  of  4  millimeters,  the  aperture  of  the  cornea  would  be  20 
degrees  ;  and  a  pupillary  diameter  of  4  millimeters  is  rather  insufficient, 
for  it  must  not  be  forgotten  that  we  generally  examine  our  patients 
with  a  very  strong  light.  In  the  ordinary  circumstances  of  life,  the 
pupillary  diameter  is  most  frequently  greater  (5  or  6  millimeters),  whence 
results  a  series  of  errors  which  would  be  still  greater  but  for  the  special 
precautions  taken  to  neutralize  them  in  part. 

We  must  bear  in  mind  that  the  pupil  is  seen  neither  in  its  real  posi- 
tion nor  at  its  true  size  :  it  appears  moved  forward  and  enlarged  on  ac- 
count of  the  refraction  through  the  cornea.  It  is  easy  to  determine  its 
apparent  place  and  size.  In  our  general  formula,  -^  -f-  -^-  =  1,  we  must 
put  the  values  of  the  cornea  of  the  simplified  eye,  F±  =  24,  F2  =  32,  and 
the  distance  of  the  anterior  surface  of  the  crystalline  lens  and  of  the  pupil 
from  the  anterior  surface  of  the  cornea,  f2  =  3.6,  and  we  find  /x  =  —  3.04. 
And  if  the  real  size  is  4  millimeters,  we  put  in  the  formula  -£-  =  L  the 
values 

O  =  4mm,  F2  =  32mm,  /2  =  3.6mm  —  32mm  =  —  28.4mm  ; 
therefore 


The  pupil  appears,  therefore,  moved  forward  about  0.5  mm.  and  en- 
larged by  the  same  quantity.  The  iris  appears  at  the  same  time  swelled 
in  front. 

What  we  see  is,  therefore,  a  virtual  image  of  the  iris  and  of  the 
pupil.  We  call  these  images  apparent  iris  and  apparent  pupil.  They  are 
aerial  images.  Rays  which,  in  the  air,  are  directed  towards  a  point  of 
the  apparent  pupil  are,  after  refraction  by  the  cornea,  directed  towards 
the  corresponding  point  of  the  real  pupil. 

If  we  imagine  the  iris  and  pupil  seen,  through  the  crystalline  lens,  by 
an  eye  located  in  the  vitreous  body,  the  pupil  would  no  longer  appear 


THE  OPTIC  SYSTEM  OF  TEE  EYE  35 

in  its  place,  but  the  displacement  would  be  less ;  it  would  be  seen  nearly 
o.i  mm.  farther  back  than  it  is  in  reality,  and  enlarged  0.2  mm.  Rays 
coming  from  a  point  of  the  real  pupil  would  proceed  in  the  vitreous 
body  as  if  they  came  from  the  corresponding  point  of  the  crystalline 
image. 

If  we  had  constructed  the  corneal  image  and  the  crystalline  image 
of  a  point  of  the  pupil,  we  would  then  know  that  a  ray  directed  towards 
the  former  would  pass,  after  refraction  by  the  cornea,  through  the  same 
point,  and,  after  refraction  by  the  crystalline  lens,  through  the  crystal- 
line image  of  the  point.  The  apparent  pupil  belongs  therefore  to  the 
incident  rays  as  does  the  first  principal  point  or  the  first  nodal  point, 
and  the  crystalline  image  of  the  pupil  belongs  to  the  emergent  rays. 

The  luminous  cone  which  enters  the  eye  is  limited  by  the  apparent 
pupil;  in  its  course  between  the  cornea  and  the  crystalline  lens,  it  is 
limited  by  the  real  pupil,  and,  in  the  vitreous  body,  by  the  crystalline 
image  of  the  pupil.  There  are  analogous  phenomena  in  most  optical 
instruments,  wherever  a  diaphragm  is  between  two  lenses;  Professor 
Abbe  has  proposed  the  names  of  pupil  of  entrance  and  pupil  of  exit  for 
the  images  of  the  diaphragm. 

We  have  seen  that  the  principal  planes  are  each  the  image  of  the 
other,  and  that  they  have  this  characteristic  that  the  object  and  image 
are  of  the  same  size. 

In  the  formula  -|X  -f-  -£  =  1,  the  distances  marked  1  are  calculated 
to  start  from  the  first  principal  point,  those  marked  2  to  start  from  the 
second  principal  point.  But  in  this  formula  we  can  as  well  calculate  the 
distances  from  any  other  pair  of  points,  one  of  which  is  the  image  of  the 
other.  We  might  measure,  for  example,  from  the  pupil  of  entrance  and 
pupil  of  exit.  We  would  thus  have  in  figure  27  the  relation  ~~  +  ^  =1 


Fig.  27.  —  oa,  pupil  of  entrance;  66,  pupil  of  exit;  O,  object;  I,  image;  4>1}  anterior 

focus ;  4>j,  posterior  focus. 

and  we  could  find  the  image  of  an  object  by  constructions  analogous  to 
those  in  which  we  have  used  the  principal  planes.  The  only  difference 
is  this:  if  an  incident  ray  meets  the  first  principal  plane  at  a  distance 


36  PHYSIOLOGIC  OPTIC8 

from  the  axis  equal  to  y,  the  emergent  ray  also  cuts  the  second  princi- 
pal plane  at  a  distance  from  the  axis  equal  to  y.  But  if  the  incident  ray 
meets  the  pupil  of  entrance  at  a  distance  from  the  axis  equal  to  y,  the 
emergent  ray  cuts  the  plane  of  the  pupil  of  exit  at  a  distance  from  the 
axis  which  is  to  y  in  the  same  relation  as  the  diameter  of  the  pupil  of 
exit  is  to  that  of  the  pupil  of  entrance.  In  our  case  it  would  be  the  re- 
lation of  -g-.  This  mode  of  procedure  is  often  more  convenient  than 
the  classic  method,  more  especially  because  it  is  easy  by  this  construc- 
tion to  calculate  the  diameter  of  the  luminous  cone. 

19.  Point  of  Fixation.    Visual  Line.  —  To  distinguish  an  object  clearly 
it  is  necessary  to  fix  it,  that  is  to  say,  to  place  the  eye  in  such  a  way 
that  its  image  is  formed  on  the  fovea.    The  point  fixed  and  the  fovea 
are  therefore  conjugate  foci.     But  we  would  be  greatly  deceived  if  we 
thought  that  the  entire  fovea  corresponded  with  the  point  of  fixation.  The 
anatomical  fovea  has  an  extent  of  0.2  mm.  to  0.4  mm.  (Henle)  or  of  0.75° 
to  1.50°,  seen  from  the  posterior  nodal  point  (at  1 6  millimeters  from  the 
retina).     Looking  at  the  sky  the  fovea  would  cover,  therefore,  a  part 
having  two  or  three  times  the  diameter  of  the  moon,  which  corresponds 
to  a  half  degree.    The  point  of  fixation  is  much  smaller  in  dimension, 
for  'we  can  readily  tell  whether  we  fix  the  right  border  or  the  left  border 
of  the  moon.    Generally  when  two  points  closely  approach  each  other 
we  can  still  tell  which  one  is  fixed  as  long  as  we  can  see  that  there  are 
two.     It  was  Javal  who  specially  insisted  on  this  fact,  to  which  he  at- 
tributed great  importance  for  the  theory  of  binocular  vision. 

We  designate  as  the  visual  line  the  ray  which  goes  from  the  point  fixed 
to  the  first  nodal  point,  and  which,  consequently,  after  refraction, 
reaches  the  fovea  as  if  it  came  from  the  second  nodal  point.  If,  in  the 
aphakic  eye,  we  neglect  the  posterior  surface  of  the  cornea,  the  visual 
line  passes  through  the  center  of  curvature  of  the  anterior  surface ;  it  is, 
therefore,  perpendicular  to  that  surface.  In  a  normal  eye  it  is  never  far 
from  being  so,  since  the  nodal  points  are  very  near  the  center  of  curva- 
ture of  the  anterior  surface  of  the  cornea.  The  direction  of  the  visual 
line  does  not  depend  on  the  position  of  the  pupil.  In  cases  of  pupillary 
displacement  it  may  happen  that  the  ray  which  represents  the  visual 
line  does  not  enter  the  eye.  We  shall  see  later  (page  64)  how  we  may 
determine  experimentally  the  direction  of  the  visual  line  in  the  eye. 

20.  Optic  Axis.     Angle  «.  —  An  exact  centering  would  demand  that 
the  four  centers  of  curvature,  or  the  three,  if  we  neglect  the  posterior 


THE  OPTIC  SYSTEM  OF  THE  EYE  3T 

surface  of  the  cornea,  would  be  on  the  same  straight  line.  The  center- 
ing of  the  eye  is  never  exact,  but  the  deviations  that  we  can  establish 
are  often  small.  In  some  cases  I  have,  however,  found  defects  of  cen- 
tering relatively  large  in  eyes,  too,  which  functionally  should  be  con- 
sidered normal.  The  defect  which  I  have  most  frequently  met  consists 
in  this,  that  the  center  of  curvature  of  the  cornea  is  situated  (as  much  as 
a  quarter  of  a  millimeter)  below  the  axis  of  the  crystalline  lens.  —  Neg- 
lecting these  deviations  the  optic  system  of  the  eye  may  be  considered 
as  centered  around  a  straight  line  which  is  called  the  optic  axis  of  the 
eye.  The  fovea  not  being  placed  on  this  line,  it  does  not  coincide  with 
the  visual  line ;  it  is  directed  outward  and  downward  from  the  visual  line 
and  forms  with  it  an  angle  of  5°  to  7°,  called  the  angle  «  (fig.  21).  — 
We  shall  see  later  that  the  anterior  surface  of  the  cornea  is  not  spher- 
ical: it  is  flattened  towards  the  periphery  so  that  it  may  be  compared 
to  an  ellipsoid  of  revolution  around  the  long  axis.  Certain  authors 
designate  as  the  angle  «  the  angle  which  the  line  of  vision  forms  with 
that  axis  which  passes  through  the  most  curved  part  of  the  cornea  (the 
summit).  Generally  the  axis  of  the  cornea  very  nearly  coincides  with  the 
optic  axis  of  the  eye,  so  that  both  definitions  amount  to  the  same  thing. 
But  we  shall  see  that  the  comparison  of  the  form  of  the  cornea  to  that 
of  an  ellipsoid  is  very  defective.  Hence  it  may  be  better  to  retain  the 
old  definition. 

We  can  compare  the  optic  system  of  the  eye  with  that  of  an  opera 
glass.  If  the  optician,  by  a  defect  of  workmanship,  had  placed  one  of 
the  lenses  a  little  obliquely,  or  if  he  had  placed  the  middle  of  this  lens 
a  little  outside  the  axis  of  the  instrument,  this  defect  would  correspond 
with  a  defect  in  the  centering  of  the  eye.  —  If,  on  the  contrary,  the  ob- 
server looked  a  little  obliquely  through  the  glass,  the  visual  line  would 
form  with  the  axis  of  the  glass  an  angle  which  would  correspond  with 
the  angle  «. 

21.  Useful  Image.  —  The  optic  system  of  the  eye  forms  a  dioptric 
image,  real,  inverted  and  diminished,  which  is  projected  on  the  retina  as 
the  photographic  image  is  formed  on  the  screen  of  the  dark  chamber. 
The  comparison  between  the  eye  and  the  dark  chamber  dates  from  the 
invention  of  this  instrument  (Porta,  Leonardo  da  Vinci).  But  although  we 
had  from  that  time  all  the  elements  necessary  to  understand  the  construc- 
tion of  the  eye,  there  continued,  however,  to  prevail  much  confusion  on 
this  question,  more  especially  because  people  could  not  be  brought  to 
admit  that  the  image  which  serves  for  vision  was  inverted.  It  was 


38  PHYSIOLOGIC  OPTICS 

Kepler  (1604)  who  first  explained  the  formation  of  images  in  general 
and  was  led  to  suppose  the  existence  of  an  inverted  image  on  the  retina, 
an  image  which  was  later  demonstrated  by  Scheiner  on  an  eye  from 
which  he  had  removed  a  part  of  the  sclera  and  of  the  choroid.  —  But, 
besides  this  image  which  I  designate  as  the  useful  image,  because  it 
serves  for  vision,  there  is  formed  in  the  eye  a  series  of  other  images 
which  I  have  designated  as  false  images  of  the  eye,  and  which  will  form 
the  subject  of  the  following  chapter: 

Bibliography.  —  (Euvres  ophthalmologiques  of  Thomas  Young,  edited  by  Tscherning, 
p.  134-137.  —  Listing  (J.).  Dioplrik  des  Auges  in  Wagner,  Handwb'rterbuch  der  Physiologic. 
—  Tscherning  (M.).  Beitrdge  zur  Dioptrik  des  Auges  in  Zeitschrift  fur  Psychologie  und  Phys- 
iologie  der  Sinnesorgane,  III,  p.  429.  —  Matthiessen.  Die  neueren  Fortschritte  in  unserer  Kent- 
niss  von  dem  optischen  Baue  des  Auges  der  Wirbelthiere  in  Beitrdge  zur  Psychologie  und  Phys- 
iologie  der  Sinnesorgane,  dedicated  to  Helmholtz  on  the  occasion  of  his  70th  anniversary. 
Stadtfeldt  (A.).  Hecherches  sur  I'indice  total  du  cristallin  humain.  Journal  de  Physiologie  et 
Pathologic.  November,  1899. 


CHAPTER  III. 
FALSE  IMAGES  OF  THE  EYE. 

22.  General  Kemarks.  —  If  we  place  a  flame  at  some  distance  from  a 
lens,  we  notice  on  the  same  side  with  the  light  two  reflected  images  of 
the  flame,  one  for  each  surface.  Placing  the  eye  on  the  other  side  of  the 
lens  at  some  distance,  we  see  the  dioptric  image,  which  is  real,  and, 
besides,  a  small,  indistinct  image  due  to  a  double  reflection  in  the  in- 


incident  Ray 


Ray 


Harmful  Ray 
Useful  Ray , 

>  i^ost  Ray 
Fig.  28.  —  Reflections  and  refractions  by  a  lens. 

terior  of  the  lens,  a  first  reflection  produced  by  the  posterior  surface, 
and  a  second  by  the  anterior  surface  (fig.  28).  The  rays  which  form  this 
latter  image  undergo,  besides,  a  refraction  by  each  surface  of  the  lens. 
The  small  image  is  real ;  we  can,  indeed,  receive  it  on  a  screen  held  near 
the  lens. 

The  incident  light  is  thus  divided  into  three  portions:  useful  light 
which  forms  the  dioptric  image  of  which  we  generally  make  use,  the 
light  lost  by  reflection  on  the  surfaces,  and  lastly,  the  light  reflected  twice, 
which  I  call  harmful  (nuisible).  This  harmful  light  may,  indeed,  enter  the 
eye  which  is  observing  the  useful  image,  where  it  is  often  a  cause  of 

89 


40 


PHYSIOLOGIC  OPTICS 


annoyance,  because  it  does  not  contribute  to  the  formation  of  that 
image.  A  simple  lens  loses  about  8  per  cent,  by  reflection,  and  the 
harmful  light  represents  only  1/500  of  the  incident  light.  In  complicated 
instruments  much  more  of  the  light  is  lost.  In  the  ophthalmometer  of 
Javal  and  Schioetz,  the  loss  is  about  33  per  cent. 

In  the  human  eye  we  may  also  distinguish  between  the  useful  light 
which  passes  through  the  surfaces,  the  light  lost  by  reflection,  and  the 
harmful  light,  which,  having  suffered  two  reflections,  returns  again 
towards  the  retina.  But  the  eye  has  this  peculiarity  that,  of  all  optic 
instruments,  it  is  that  which  loses  least  light  (about  2  per  cent.).  The 
harmful  light  is  also  reduced  to  a  minimum,  but  feeble  as  it  is,  it  is 
visible  nevertheless. 

The  useful  light  forms  the  dioptric  image  which  serves  the  purpose  of 
vision;  the  lost  light  forms  four  false  images  of  the  first  order,  called 


Fig.  29.  —  Manner  in  which  a  luminous  ray  is  divided  in  the  eye. 

A,  incident  ray.  —  I,  II,  III,  IV,  lost  rays  corresponding  to  the  four  images  of  Purkinje; 
V  and  VI,  harmful  rays  corresponding  to  the  fifth  and  sixth  image ;  VII,  useful  ray. 

images  of  Purkinje,  one  for  each  surface ;  they  correspond  to  rays  I,  II, 
III  and  IV,  fig.  29.  The  harmful  light  forms  a  series  of  false  images 
of  the  second  order,  of  which  one  only  is  visible  (rays  V  and  VI,  fig.  29). 

23.  The  Images  of  Purkinje.  —  These  images  were  described  at  the 
beginning  of  this  century  by  the  scientist  whose  name  they  bear,  but 
one  of  them,  the  second,  was  lost  sight  of  until  I  described  it  again 
some  years  ago.  (i)  The  first  of  these  images,  that  due  to  the  anterior 
surface  of  the  cornea,  is  produced  by  a  single  reflection,  the  others  are 
formed  by  rays,  which,  after  having  suffered  one  or  several  refractions, 
are  at  first  reflected,  then  undergo  still  other  refractions  before  emerg- 
ing from  the  eye.  The  optic  systems  which  produce  these  images  are, 
therefore,  quite  complicated,  but  we  can  always  replace  them  by  a  single 
reflecting  surface,  which  I  call  the  apparent  surface. 

(1)  See  Biix,  however.    Oftalmometriska  Studier.    Uppsala,  1880,  p.  63. 


FALSE  IMAGES  OF  THE  EYE 


41 


Suppose,  for  example,  that  we  wish  to  study  the  third  image  of 
Purkinje,  that  produced  by  reflection  at  the  anterior  surface  of  the  crys- 
talline lens.  Neglecting  the  weak  refraction  by  the  posterior  surface  of 
the  cornea,  the  rays  suffer,  besides  reflection,  two  refractions,  one  on  en- 
tering and  the  other  on  emerging  from  the  eye.  Now,  we  can  replace 


Fig.  30.  —  Position  of  the  seven  images  in  the  eye.     The  object  is  supposed  to  be  situated 
at  20  degrees  below  the  yisual  line. 

this  series  of  refractions  and  reflections  by  a  simple  reflection  on  the  ap- 
parent surface.  We  find  the  position  of  this  surface  by  finding  the  posi- 
tion of  the  image  of  the  real  surface,  seen  through  the  cornea,  in  the 
same  manner  as  we  have  already  found  the  position  of  the  apparent 
pupil,  by  means  of  the  formula  ^  +  -jf-  =  1 ;  with  the  values  of  the 
simplified  eye  we  have  F±  =  24  mm.,  F2  =  32  mm.,  f2  =  3.6  mm.,  which 
gives  the  position  of  the  apparent  surface,  f±  =  —  3  mm.  We  then  find 
the  position  of  the  center  of  the  apparent  surface  by  finding  in  the  same 
manner  the  image  of  the  center  of  the  real  surface  seen  through  the 
cornea  (f±  =  13.5,  which  gives  fz  =  —  17.5).  The  apparent  surface  being 
at  3  mm.  and  its  center  at  17.5  mm.,  it  must  perform  the  function  of  a 
convex  mirror  of  14.5  mm.  radius,  placed  three  millimeters  behind  the 
cornea.  The  focus  is  at  an  equal  distance  between  the  surface  and  the 
center,  that  is  to  say  at  10.2  mm.  behind  the  cornea;  it  is  therefore  very 
nearly  at  this  place  that  the  third  image  of  Purkinje  is  formed.  We  can 
also  use  the  apparent  surface  to  calculate  the  size  of  the  image,  follow- 
ing the  formula-?-  =  ~  (see  page  5.) 

To  make  the  same  calculation  for  the  posterior  surface  of  the  crys- 
talline lens,  we  must  first  calculate  the  refracting  system  composed  of 
the  cornea  and  of  the  anterior  surface  of  the  crystalline  lens,  and  then  the 


42  PHYSIOLOGIC  OPTICS 

images  of  the  posterior  surface  and  of  its  center,  seen  through  this 
system.  —  With  the  exception  of  the  anterior  surface  of  the  crystalline 
lens,  the  apparent  surfaces  differ  only  slightly  from  the  real  surfaces. 

The  three  first  surfaces  being  convex  their  images  are  erect,  while 
that  of  the  fourth  is  inverted.  —  The  object  being  generally  at  quite  a 
distance,  the  images  are  formed  very  near  the  catoptric  foci  of  the 
apparent  surfaces.  The  first,  second  and  fourth  are  nearly  in  the  pupil- 
lary plane,  while  the  third  is  situated  at  7  or  8  mm.  behind  this  plane 
(fig.  30).  —  Besides,  the  third  image  easily  disappears  behind  the  iris 
when  the  eye  makes  a  slight  movement,  which  makes  this  image  more 
difficult  to  observe  than  the  others. 

24.  Manner  of  Observing  the  Images  of  Purkinje.  —  The  first  linage, 
that  of  the  anterior  surface  of  the  cornea,  is  much  the  brightest;  its 
observation  offers  no  difficulty. 

To  observe  the  second  image  we  place  ourselves  as  when  we  wish  to 
examine  a  patient  by  oblique  illumination,  and  we  examine  the  eye  with 
a  magnifying  glass,  a  lens  of  10  D.  for  example,  but  without  concentrat- 
ing the  light  on  the  eye. 

Examining  the  corneal  image  of  the  flame,  we  shall  see  when  it 
approaches  the  border  of  the  pupil,  and  still  better,  when  it  shall  have 
passed  it,  that  it  is  accompanied  by  a  small  image  which  is  situated  near 
it.  The  more  the  images  approach  the  edge,  the  more  distant  they  are 
from  each  other;  near  the  edge  the  distance  may  exceed  a  millimeter, 
and  the  small  one  is  frequently  still  visible  when  the  large  one  has 
already  disappeared,  giving  way  to  the  irregular  reflex  of  the  sclera. 

The  small  image  is  always  situated  between  the  large  image  and  the 
middle  of  the  pupil,  which  indicates  that  the  posterior  surface  is  more 
curved  than  the  anterior  surface.  Suppose,  indeed,  that  we  used  two 
lamps,  one  on  each  side,  and  consider  the  distance  separating  the  two 
lamps  as  the  object  (fig.  31).  It  is  then  clear  that  the  image  of  the 
posterior  surface  is  smaller  than  that  of  the  anterior  surface,  which  indi- 
cates that  its  curvature  is  greater.  At  the  middle  of  the  pupil  the  small 
image  is  not  visible,  because  it  coincides  with  the  large  one ;  they  are, 
indeed,  situated  at  the  same  distance  from  the  summit  of  the  cornea. 

The  third  image,  the  largest,  always  preserves,  whatever  we  may  do, 
a  more  or  less  diffuse  appearance,  due  to  the  fact  that  the  index  varies 
in  the  superficial  layers  of  the  crystalline  lens.  To  observe  it  we  place 
ourselves  as  before,  requesting  the  person  whose  eye  is  being  examined 
to  look  in  a  direction  which  nearly  bisects  the  angular  distance  between 
the  eye  of  the  observer  and  the  flame.  By  moving  his  eye  slightly  from 


FALSE  IMAGES  OF  THE  EYE  43 

side  to  side  the  observer  will  quite  easily  see  the  image  which  presents 
itself  as  a  broad  glow,  pale  and  more  or  less  diffuse,  and  which  changes 
position  at  the  least  movement  of  the  observed  eye. 


Fig.  31.  —  Corneal  images  of  two  lamps,  observed  with  the  ophthalmophakometer.  The 
small  images  beside  the  large  ones  are  due  to  reflection  by  the  posterior  surface  of  the 
cornea. 


After  having  found  the  image,  we  can  concentrate  the  light  on  the 
eye;  by  this  means  we  magnify  the  image,  which  soon  fills  the  entire 
pupil.  If  the  light  is  bright  the  pupil  frequently  appears  white,  as  if 
the  eye  was  affected  by  a  ripe  cataract,  and  we  may,  by  examining  it 
with  the  magnifying  glass,  thus  observe  anatomical  details  which  we 
cannot  discover  in  any  other  way.  I  recommend  to  clinicians  this  exam- 
ination, of  which  I  have  nowhere  found  a  description,  (i)  To  make  the 
experiment  under  the  best  conditions  we  must  select  a  lens  of  large  aper- 
ture, place  the  luminous  source  at  quite  a  distance  and  hold  the  lens  in 
such  a  way  that  its  focus  coincides  with  the  catoptric  focus  of  the  surface. 

The  third  image  is,  as  we  shall  see,  of  great  importance  for  the  study 
of  accommodation. 

The  fourth  image  does  not  generally  offer  any  difficulties  to  the  ob- 
server. —  It  is  observed  under  the  same  conditions  as  the  preceding  one, 
by  directing  the  look  of  the  observed  person  a  little  towards  the  lamp. 


(1)  Rings  of  DEMICHERI.  —  Demicheri  has  recently  (Bulletin  of  the  Society  of  Ophthalmology  of  Paris) 
described  phenomena  of  coloration  which  are  observed  by  this  method  in  the  pupil  in  certain  affections 
of  the  crystalline  lens.    The  middle  of   ' 
zone,  then  by  a  yellow  zone,  and  lastly 
eration  was  one  of  more  or  less  mature  cataract. 

over,  the  crystalline  lens  appeared  intact,  the  pupil  was  tilled  by  this  examination  with  an  intense  red, 
so  that  one  would  have  thought  it  filled  with  blood.  —  These  colors  are  probably  phenomena  of  inter- 
ference due  to  the  reflection  on  the  finely  reeded  surface  of  the  crystalline  mass,  nearly  like  the  colors 
which  mother-of-pearl  presents,  but  the  conditions  under  which  they  are  produced  are  still  unknown. 


loratiou  which  are  observed  by  tins  memoa  in  tne  pupil  in  certain  affections 
e  middle  of  the  pupil  appeared  blackish  blue  ;  it  was  surrounded  by  a  green 
»,  and  lastly  by  a  red  zone,  near  the  pupillary  border.  The  case  under  cotisid- 
less  mature  cataract.  In  a  case  which  I  have  examined,  and  in  which,  more- 


44 


PHYSIOLOGIC   OPT! CIS 


It  is  small  and  distinct.    Being  inverted  it  moves  in  a  direction  contrary 
to  that  of  the  others. 

For  a  more  minute  examination  of  these  images  my  ophthalmophako- 
meter  may  be  used  (fig.  32).    It  is  composed  of  a  small  telescope,  sup- 


.  32 — The  Ophthalmophakometer. 

ported  on  a  stand,  and  of  a  copper  arc  movable  around  the  axis  of  the 
telescope,  and  bearing  a  scale,  the  zero  of  which  coincides  with  this  axis. 
The  radius  of  the  arc  is  86  centimeters.  The  head  of  the  observed 
person  is  fixed  by  a  head-rest  in  such  a  manner  that  the  eye  which  we 
are  to  examine  is  at  the  center  of  the  arc.  —  On  the  arc  move  several 
cursors,  which  carry  electric  lamps.  Each  lamp  is  enclosed  in  a  tube 
closed  in  front  by  a  plano-convex  lens,  which  concentrates  the  light 
on  the  observed  eye.  —  I  will  speak  later  of  the  manner  of  using  the 
instrument  for  measuring  the  internal  surfaces  of  the  eye. 

25.  False  Images  of  the  Second  Order.  —  All  the  reflected  rays  which 
emerge  from  the  eye  to  form  the  images  of  Purkinje,  with  the  exception 
of  those  of  the  first  image,  meet  surfaces  which  again  reflect  a  part  of 
the  light;  this  light  is  extremely  feeble  for  most  of  the  surfaces;  it  is 
only  on  meeting  the  anterior  surface  of  the  cornea  that  there  is  reflected 
sufficient  light  to  be  visible.  Thus  there  are  formed  two  more  images, 
the  fifth,  produced  by  a  first  reflection  on  the  anterior  surface  of  the 
crystalline  lens,  and  a  second  reflection  on  the  anterior  surface  of  the 


FALSE  IMAGES   OF  THE  EYE  45 

cornea,  and  the  si.vth,  due  to  a  first  reflection  on  the  posterior  surface 
of  the  crystalline  lens  and  a  second  reflection  on  the  anterior  surface  of 
the  cornea.  —  As  the  rays  return  towards  the  retina,  these  images  are 
subjective. 

The  optic  systems  which  produce  these  images  are  very  complicated. 
They  are  calculated,  too,  by  the  formulae  which  we  have  explained  on 
page  21.  The  focus  of  the  fifth  image  is  near  the  posterior  surface  of 
the  crystalline  lens.  It  is,  therefore,  at  this  place  that  this  image  of  a 
distant  object  is  formed.  Before  reaching  the  retina  the  rays  are  so 
dispersed  that  they  are  no  longer  visible ;  I,  at  least,  have  not  been  able 
to  discover  the  least  trace  of  this  image.  Theoretically  we  ought  to  be 
able  to  make  it  visible  by  bringing  the  object  nearer,  since  the  image 
and  object  move  in  the  same  direction  as  in  all  the  refracting  systems, 
but  the  experiment  did  not  succeed.  In  fact,  when  the  flame  with  which 
we  are  working  is  moved  near  enough  to  the  eye,  the  useful  image 
becomes  transformed  into  a  diffusion  circle,  which  fills  the  greater  part 
of  the  field  and  prevents  one's  seeing  anything  else. 

The  focus  of  the  sixth  system  is,  on  the  contrary,  very  near  the  retina 
of  the  emmetropic  eye ;  the  image  is  also  generally  easy  to  observe. 

26.  Manner  of  Observing  the  Sixth  Image.  —  We  choose,  in  a  half- 
darkened  room,  a  point  of  fixation  situated  some  distance  away,  and, 
having  fixed  this  point,  we  give  to  the  candle,  held  in  the  hand,  a  to-and- 
fro  horizontal  motion,  moving  it  towards  and  away  from  the  visual 
line  without,  however,  reaching  it. 

We,  then,  notice  on  the  other  side  of  the  visual  line  a  pale  image  of  the 
flame.  Some  people  see  the  phenomenon  sufficiently  distinct  to  be  able 
to  discern  that  the  image  appears  inverted,  the  retinal  image  being  erect. 
We  discern  more  clearly  the  form  of  the  image  when  we  cause  the  candle 
to  pass  below  the  visual  line ;  the  image  then  passes  above,  and  we  see 
that  its  apex  is  directed  downwards.  Myopes  see  the  image  with  greater 
difficulty ;  they  often  succeed  better  when  using  their  correcting  glasses, 
but  they  must  then  guard  against  confounding  it  with  the  images  pro- 
duced by  repeated  reflections  between  the  cornea  and  the  glasses. 

It  seems  that  there  are  persons  who  cannot  perform  the  experiment 
successfully.  If  the  anterior  chamber  is  unusually  deep  it  may,  indeed, 
happen  that  the  focus  of  the  system  is  quite  a  distance  from  the  retina, 
but  we  ought  then  to  be  able  to  succeed  by  moving  the  flame  towards 
the  eye  or  away  from  it. 

We  see,  therefore,  how  very  advisable  it  is  that  the  harmful  light  be 
reduced  to  a  minimum;  in  fact,  if  the  index  of  the  superficial  crystalline 


46  PHYSIOLOGIC   OPTICS 

layers  had  been  higher,  the  sixth  image  would  have  had  more  brilliancy, 
and  we  would  be  affected  with  an  annoying  monocular  diplopia.  And 
right  here  we  must  pause  to  wonder  at  the  enormous  sensitiveness  of 
the  retina,  for  the  brightness  of  the  sixth  image  is  really  only  ^m  of 
that  of  the  useful  image. 

One  can  study  the  sixth  image  more  closely,  by  means  of  the  ophthal- 
mophakometer,  by  placing  oneself  in  the  place  of  the  person  examined, 
and  by  fixing  the  middle  of  the  objective  of  the  telescope,  which  cor- 
responds to  the  zero  of  the  division. 

Placing  the  arc  horizontally,  and  putting  the  lamp  A  which  slides  on 
the  arc  at  some  distance  from  the  telescope,  we  see  the  image  appear 
on  the  other  side.  We  bring  one  of  the  cursors  of  the  arc  to  coincide 
with  the  image,  so  that  we  may  read  its  position  on  the  scale.  We,  then, 
notice  that  the  image  is  only  approximately  symmetrical  with  the  lamp, 
in  relation  to  the  visual  line.  By  causing  the  arc  to  rotate  180°  in  such  a 
way  as  to  bring  the  lamp  into  a  position  symmetrical  with  the  former,  we 
notice  that  the  image  no  longer  coincides  with  the  cursor.  This  is  on 
account  of  the  angle  «.  If  the  visual  line  coincided  with  the  optic  axis, 
the  two  positions  of  the  image  corresponding  to  two  positions  sym- 
metrical with  the  lamp,  ought  to  be  symmetrical.  We  can  use  measure- 
ments of  this  kind  to  determine  the  size  of  the  angle  «. 

It  was  while  using  the  ophthalmophakometer  that  I  found  this  image, 
which  I  described  as  new  in  1891.  But  Coccius  had  seen  it  previously, 
and  Otto  Becker  had  given  the  explanation  of  it  in  1860  in  a  memoir 
which  is  very  little  known.  Heuse  described  it  again  in  1872,  but  gave 
an  erroneous  explanation  of  it. 

The  images  of  Purkinje  have  no  interest  as  far  as  the  function  of  the 
eye  is  concerned,  but  they  are  of  great  importance  for  the  physiology 
of  vision.  It  is,  indeed,  by  a  study  of  them  that  we  can  determine  the 
form  and  position  of  the  refracting  surfaces  of  the  eye.  The  study  of 
these  images  constitute  ophthalmometry,  to  which  we  will  devote  our 
attention  in  the  following  chapter. 

Bibliography.  —  Purkinje  (I.  E.).  Commentatio  de  examine  physiologico  organi  visus  et 
systematis  cutanei.  Vratislaviae,  1823.  —  Becker  (O.).  Utber  Wahrnehmung  eines  Eeflexbildes 
im  eigenen  Auge,  Wiener  medicinische  Wochewchrift,  1860,  p.  670-672  and  684-688.  —  Heuse. 
Ueber  die  Beobachtung  einer  neuen  entoptischen  Erscheinung.  Oraefe's  Archiv.  Bd.  18,  2,  p.  236. 
—  M.  Blix.  Oftalmometriska  Studier.  Upsala,  1880.  —  Tscherning.  Recherches  sur  la  qua- 
riZme  image  de  Purkinje;  Arch,  de  physiol.,  1890.  —  Tscherning.  Theorie  des  images  de  Pur- 
kinje et  description  d'une  nouvelle  image.  Arch,  de  physiol,  1891.  —  Tscherning.  Sur  une 
nouvelle  image  d  la  fois  catoptrique  et  dioptriqve  de  Vcdl  humain  et  une  nouvelle  methode  pour 
determiner  la  direction  de  Paxc  optique  de  I' ceil.  Bulletin  de  la  Societe  francaise  d'ophtalmologie 
1891,  p.  203. 


CHAPTER  IV. 

OPHTHALMOMETRY. 


27.  Principles  of  Ophthalmometry.  —  The  basis  of  ophthalmometry  is 
the  formula  -2-  =  -±r=^-orR  =  ~-  (see  page  5 ).  To  determine 
the  radius  R  of  the  small  convex  mirror  which  forms  the  anterior  sur- 
face of  the  cornea,  we  measure  the  image  I  of  an  object  O,  placed  at  a 
given  distance  /.  There  is  never  any  difficulty  measuring  either  the 
object  or  the  distance;  it  is,  therefore,  to  the  measurement  of  the  image 
that  we  must  devote  our  attention. 

We  may  say  at  once  that  we  generally  use  as  objects  the  distances 
separating  two  flames  or  two  white  objects  (mires).  The  image,  then, 
is  the  distance  separating  the  images  of  the  flames  or  of  the  mires. 

The  method  most  used  by  physicists  for  such  measurements  consists 
in  placing  a  micrometer  at  the  focus  of  the  objective  of  the  telescope 
with  which  the  image  is  observed.  The  objective  forms  an  image  which 
coincides  with  the  micrometer,  the  graduations  of  which  permit  the 
size  of  the  image  to  be  read  directly  by  observing  it  through  the  eye 
piece.  It  has  been  attempted  to  use  this  method  for  ophthalmometry, 
but  without  success.  As  the  observed  eye  cannot  be  kept  absolutely 
quiet,  the  image  is  constantly  changing  its  place  in  relation  to  the  mi- 
crometer, which  makes  a  fairly  exact  measurement  impossible. 

This  is  why  Helniholts  introduced  into  ophthalmometry  another  prin- 
ciple which  he  borrowed  from  astronomy,  where  the  same  problem 
present  itself,  that  of  doubling  (dedoublement).  It  seems,  however,  that 
the  method  had  already  been  used  for  the  same  purpose  by  Thomas 
Young. 

Suppose  that  we  desire  to  measure  the  distance  I  separating  the  two- 
points  a  and  b  (fig.  33,1),  and  that  we  have  a  process  which  permits  us 
to  see  everything  doubled  at  a  certain  distance  D.  By  this  means  in- 
stead of  the  two  points  a  and  b  we  would  see  four,  a^  and  a2,  b^  and  b2t. 

47 


48  PHYSIOLOGIC  OPTICS 

and  the  distance  ax  a2  would  be  equal  to  b^  b2  and  to  D,  while  the  dis- 
tance at  bi  =  a2b2  =  l  (fig.  33,2). 

Suppose,  now,  we  could  make  the  doubling  vary.     By  increasing  it 
we  would  reach  a  point  when  a2  and 
b^   would   coincide    (fig.    33,3)    which 
would  take  place  at  the  moment  when    l  <t 

I  would  be  equal  to  D.     If  we  knew 

the    amount    of    doubling    used    we  r.-- --%  « 

would    thus    have    measured  I  —  ab,  ^  -----  ^ 

and   our    object   would   be    attained. 

When  a  and  b  touch  we  say  that  we  &  • 

have  obtained  contact.     If  we  use  as  \ii>~' 

objects  separated  flames  so  that  a  and 

Of 

b  form  two  luminous  points  we  ob- 
tain more  exact  measurements  by  giv-     '*  J 
ing  one  of  them  the  form  of  two  points                        ^ 
situated    on   the    same    vertical    (fig. 
33,4);  at  the  moment   of   contact  the 
image  of  b  is  placed  exactly  between  the  two  points  a. 

Instead  of  making  the  doubling  vary,  we  can  make  I  vary,  which 
is  brought  about  by  varying  the  object  (displacing  one  of  the  lamps) 
until  contact  is  obtained. 

Generally  it  is  useful  to  employ  a  certain  degree  of  magnification  in 
order  to  have  easy  measurements,  and  this  suggests  the  use  of  a  tele- 
scope placed  at  some  distance  from  the  eye;  instruments  with  short 
focus,  more  or  less  resembling  microscopes,  are  not  practical  because 
it  is  impossible  to  keep  them  in  focus,  the  observed  eye  not  being  able 
to  remain  sufficiently  quiet. 

Thus,  we  would  only  have  to  affix  our  doubling  apparatus  to  our  tele- 
scope and  place  conveniently  two  flames  or  two  white  surfaces  which 
would  serve  us  as  objects,  and  we  would  be  ready  to  begin  our  measure- 
ments. 

28.  Methods  of  Doubling  (Dedonblement).  —  a)  A  first  method  consists 
m  dividing  the  luminous  cone  which  meets  the  objective,  into  two  halves, 
an  upper  and  a  lower,  and  displacing  each  half  laterally,  one  to  the  right, 
the  other  to  the  left.  We  can  obtain  this  effect : 

i°.  By  placing  before  the  upper  half  (i)  of  the  objective  a  weak  prism, 
apex  to  the  right,  and  before  the  lower  half  another,  apex  to  the  left. 


(1)  I  am  supposing  here  and  in  what  follows  that  it  is  the  horizontal  meridian  we  are  measuring. 


OPHTHALMOMETR7  49 

2°.  Instead  of  prisms  we  can  use  plane  parallel  plates,  placed  obliquely 
but  in  a  symmetrical  manner  in  relation  to  the  axis  of  the  telescope. 
Such  plates  placed  obliquely  (see  page  10)  have  the  effect  of  displacing 
the  object  laterally,  each  on  its  own  side;  the  effect  is,  therefore,  the 
same  as  that  of  prisms,  and  the  plates  give  better  images.  —  This  is  the 
system  employed  by  Helmholtz,  who  made  the  doubling  vary  by  changing 
the  inclination  of  the  plates,  and  later  by  Leroy  and  Dubois,  who  used  a 
constant  doubling  by  making  the  object  vary. 

3°.  We  can  saw  the  objective  in  two  and  displace  the  upper  half  a 
little  to  the  left,  the  lower  half  a  little  to  the  right  (fig.  34).  It  is  easy 
to  see  that  this  method  must  produce  a  doubling  of  the 
f  ^\.  image,  since  the  optic  center  of  the  objective  is,  so  to 
speak,  divided  into  two  halves,  displaced  laterally  in  rela- 
tion to  each  other.  This  method  gives  very  good  images 
and  less  light  is  lost,  since  we  obviate  the  reflection  on  the 
surfaces  of  the  prisms  or  plates,  but  the  instrument  is  very 
difficult  to  construct;  the  displacement  of  the  two  halves  of  the  objec- 
tive, in  relation  to  each  other,  must  be  made,  indeed,  with  an  exactness 
that  is  expressed  in  hundredths  of  a  millimeter. 

None  of  these  methods  is  very  practical,  because  all  of  them  call  for 
a  very  exact  adjustment  of  the  instrument  to  find  the  meridians  of  the 
astigmatic  eye  (see  ch.  IX).  —  If  the  eye  is  displaced  a  little  during  the 
measurement,  we  may  find  false  directions  for  these  meridians.  Helm- 
holtz  remedied  this  inconvenience  by  placing  himself  very  far  (at  I  or  2 
meters)  from  the  patient,  which  calls  for  a  room  prepared  for  this  pur- 
pose and  makes  measurement  pretty  difficult. 

b)  A  second  method  consists  in  dividing  the  objective  into  two  lateral 
halves,  and  displacing  laterally  each  half  of  the  incident  luminous  cone. 
Such  an  arrangement  can  be  obtained : 

i°.  By  placing  in  front  of  the  objective  a  double  prism  with  apex  ver- 
tical ; 

2°.  By  placing  before  each  half  of  the  objective  a  plate  with  plane, 
parallel  surfaces,  forming  an  angle  with  the  axis  of  the  telescope  (fig. 

35)- 

These  are  the  plates  of  Helmholtz  which  are  placed  side 
by  side  instead  of  being  placed  one  above  the  other. 

3°.  We  can  obtain  the  same  effect  by  removing  a  vertical 
band  from  the  middle  of  the  objective  and  cementing  to-        Flg'  ^ 
gather  the  remaining  parts  (fig.  36). 

Systems  of  this  order  offer  no  difficulty  in  finding  the  meridians,  but 


50 


PHYSIOLOGIC  OPTICS 


Fig.  36. 


they  have  another  inconvenience :  contact  depends  much  on  the  exact- 
ness of  the  adjustment.  If,  after  having  ob- 
tained contact  the  observed  eye  is  displaced 
a  little,  so  that  the  instrument  is  no  longer 
exactly  in  focus,  contact  ceases.  We  may 
thus  obtain  totally  false  measurements  of 
astigmatism  if  the  observed  eye  is  displaced 
between  the  two  measurements. 

This  inconvenience  is  partly  got  rid  of  in  the  model  of  the  Javal  and 
Schioetz  ophthalmometer  which  the  optician  Kagenaar,  of  Utrecht,  con- 
structed. It  uses  a  combination  of  the  methods  b,  1  and  &,  2,  a  combina- 
tion of  two  very  weak  prisms  forming  an  angle  between  them ;  the  apex 
of  the  prisms  is  inwards. 

c)  The  best  method,  however,  is  to  employ  doubly-refracting  crystals. 
Coccius  had  recourse  to  a  plate  of  spar ;  Javal  and  Schioets  used  a  Wollas- 
ton  prism.  This  prism  (fig.  37)  is  composed  of  two  rectangular  quartz 

prisms,   which   are   cemented 
together  so  as  to  form  a  sin- 
gle very  thick,  plane  parallel 
plate.    The  two  prisms  are  cut 
differently  in  the  crystal;  one 
*    has  the  apex  parallel   to    the 
axis  of  the  crystal,  the  other 
*'\  perpendicular  to  it.    Each  ray 

'"'d  which     passes     through     the 

Fig.  37.  —  Prism  of  Wollaaton.  prism  is  divided  into  two,  and 

each  of  the  two  new  rays  is 

deviated  a  little  so  that  they  are  nearly  symmetrical  in  relation  to  the 
incident  ray.  (i)  —  By  all  other  systems  which  I  have  mentioned  the 
incident  cone  is  divided  into  two  half  cones,  which  are  a  little  displaced 
in  relation  to  each  other;  the  prism  of  Wollaston  on  the  contrary  pro- 
duces two  entire  cones  of  half  the  intensity. 

The  instrument  of  Helmholtz  must  be  considered  as  an  instrument  for 
the  laboratory.  Investigators,  like  Danders  and  Mauthiier,  used  it  for 
measuring  the  eyes  of  some  patients,  but  its  use  was  so  difficult  that 
Mauthne?  exclaimed:  "Ophthalmometry  must  be  understood  as 
ophthalmoscopy,  only  it  is  much  more  difficult."  Besides  it  necessitates 


(1)  [A  detailed  theory  of  this  prism,  together  with  a  calculation  of  the  angles,  can  be  found  in  the 
Thtorie  de  rophtalmom&trie  de  la  cornte  by  Dr.  Tscherning  in  Javal's  M&moires  d'oplitatmomttrie,  Paris 
1891.]— W. 


OPETHALMOMETR7 


51 


a  dark  room,  and  the  complete  measurement  of  the  cornea  calls  for  not 
less  than  32  measurements.  It  is  only  by  the  labors  of  Javal  and  Schioets 
that  ophthalmometry  has  become  a  clinical  method. 

29.  The  Ophthalmometer  of  Javal  and  Schioetz.  —  The  instrument  (fig. 
38)  is  composed  of  a  telescope  which  carries  a  copper  arc  movable  around 
the  axis  of  the  telescope,  and  with  a  head-rest  on  which  the  head  of  the 
patient  is  supported;  when  the  telescope  is  adjusted  to  the  level  of  the 
eye  of  the  observed  person,  the  latter  is  at  the  center  of  the  arc.  —  Two 
white  mires  slide  along  the  arc,  and  it  is  the  distance  separating  them 
which  serves  as  the  object.  By  moving  one  of  the  mires  on  the  arc,  the 


Fig.  38.  —  Ophthalmometer  of  Javal  and  Schioetz. 

size  of  the  object  is  made  to  vary  until  it  corresponds  with  the  doubling 
of  the  prism  which  is  constant.  —  The  telescope  has  two  achromatic 
objectives  between  which  is  the  Wollaston  prism,  placed  so  a-s  to  double 
in  a  direction  exactly  parallel  to  the  plane  of  the  arc.  It  is,  besides,  pro- 
vided with  a  Ramsden  eye  piece  with  a  spider's  thread.  Each  observer 
must  begin  by  focusing  the  ocular  on  the  thread;  then  the  instrument 
is  adjusted  for  the  level  of  the  observed  eye  by  displacing  it  forwards 
or  backwards.  We  then  see  the  images  of  the  two  mires  doubled  (fig.  39), 
and  by  displacing  the  mire  on  the  right,  contact  is  obtained.  This  done 


52 


PHYSIOLOGIC  OPTICS 


we  can  read  the  distance  of  each  mire  in  degrees  from  the  axis  of  the 
telescope  on  the  scale  of  the  arc,  and  the  sum  of  the  two  figures  indicates 
the  corneal  refraction.  I  have  supposed  the  cornea  in  question  spher- 
ical, otherwise  we  would  have  to  begin  by  finding  the  principal  meridi- 
ans ;  but  I  shall  reserve  the  description  of  the  measurement  of  the  astig- 
matic eye  for  the  chapter  on  astigmatism. 

Generally  the  patient 
must  look  into  the  tele- 
scope; it  is  only  when 
we  wish  to  measure  the 
peripheral  parts  of  the 
cornea  also  that  we 
make  him  look  in  other 
directions. 

The  graduation  of  the 
arc  is  in  degrees,  but  the 
doubling  is  so  chosen 
that  each  degree  corre- 
sponds with  one  dioptry. 
This  calls  for  an  expla- 
nation. 

Javal  and  Schioetz  have 
taken  as  the  index  of 

the  aqueous  humor  1.3375  (i);  the  refracting  power  of  the  cornea  ex- 
pressed in  dioptrics  would  be,  therefore  (see  page  13) : 

03375 


or,  expressing  R  in  millimeters, 

337.5 


D  = 


"K 


and  K  = 


337.5 


With  this  formula  we  calculate  the  following  table,  which  gives  the 
relation  between  the  refracting  power  of  the  cornea,  expressed  in  diop- 
trics, and  the  radius  expressed  in  millimeters : 


Dioptrics.  Radius. 

40  D.  8.44mm 

39  D.  8.65mm 

38  D.  8.89mm 


(1)  This  value  of  n,  very  nearly  correct,  was  selected  in  order  that,  in  the  following  table,  43  D- 
would  correspond  exactly  to  7.5  mm.,  which  is  convenient  in  order  to  regulate  the  instrument  by  & 
sphere  type  of  7.5  mm. 


Refraction. 

Radius. 

Refraction. 

Radius. 

50  D. 

6.75mm 

45  D. 

7>5mm 

49  D. 

6.89mm 

44  D. 

7.67mm 

48  D. 

y.Ogmm 

43  D. 

7.85mm 

47  D. 

7.18»» 

42  D. 

8.04mm 

46  D. 

7.34mm 

41  D. 

8.23mm 

OPETEALMOMETR7  53 

Placing  the  value  which  we  have  just  found  for  R  in  the  formula 


_ 

I      '  R 
we  find 


337.5' 

in  which  formula  I  designates  the  image  which,  at  the  moment  of  con- 
tact, is  equal  to  the  doubling.  Let  us  designate  by  a  the  linear  length 
of  a  degree  ;  if  this  length  must  correspond  to  one  dioptry,  the  object 
which  corresponds  with  the  image  I  must  have  the  size  Da,  therefore 

Da   -2im 
~  337^ 

or 

2/1 


337.5 
On  the  other  hand  as  a  must  be  one  degree  long,  we  have 

1°  a 

360°  ~:    27J-J 
therefore 

2*1  2fl 


a  = 


360         337.5 
and 


In  order  that  a  degree  of  the  arc  may  correspond  with  one  dioptry, 
the  doubling  of  the  prism  must  be,  therefore,  2.94  mm.  This  is  what  has 
been  done. 

The  radius  of  the  arc  (/)  has  been  selected  so  that  the  linear  length 
of  a  degree  may  be  6  millimeters  (5  millimeters  in  the  new  model). 

In  the  last  models  of  the  instrument  certain  details  have  been  changed, 
but  the  principle  remains  the  same.  —  We  may  add,  furthermore,  that, 
in  order  to  measure  the  As,  one  of  the  mires  has  a  special  form  "in 
steps,"  each  of  which  corresponds  to  one  dioptry.  —  A  keratoscopic 
disc  enables  us  to  study  the  general  form  of  the  cornea. 

UTILIZED  PART  OF  THE  CORNEA.  —  It  is  only  a  very  small  part  of  the 
cornea  that  is  used  for  the  measurement.  Making  the  construction  in 
the  way  indicated  on  page  7  we  see  that  the  images  of  the  mires  are 
formed  by  reflection  on  two  small  parts  of  the  cornea  situated  about 
1.2  mm.  from  the  visual  line. 

Rotating  the  arc  these  two  parts  move  describing  a  concentric  ring 
around  the  visual  line.  This  ring  is  the  only  part  of  the  cornea  which 


54 


PHYSIOLOGIC  OPTICS 


sends  light  into  the  objective,  and  consequently  also  the  only  part  on 
which  the  instrument  can  give  information.  The  parts  situated  outside 
or  inside  this  ring  may  have  curvatures  quite  different  from  those  indi- 
cated by  the  instrument.  Suppose,  for  the  moment,  that  we  have  to 
do  with  a  conical  (hyperbolic)  cornea:  what  we  would  measure  would 
be  the  radius  of  BG  of  the  circle  BE  (fig.  40),  which  touches  the  surface 


Fig.  40. 

of  the  cornea  at  B  and  E  (see  page  13).  Generally  this  circle  coincides 
quite  closely  with  the  "optic"  part  of  the  cornea ;  but  if  we  want  to  make 
very  exact  measurements  we  must  always  take  into  consideration  this 
source  of  errors. 

EXACTNESS  OF  THE  MEASUREMENTS.  —  With  a  good  illumination  an 
experienced  observer  would  not  easily  be  led  astray  to  the  extent  of  a 
quarter  of  a  dioptry,  which  corresponds  to  almost  -~  of  a  millimeter  of 
error  for  the  radius.  Absolute  reliance  cannot,  therefore,  be  placed  in 
the  second  decimal  of  the  measure  of  the  radius.  Bonders  and  Homer 
arrived  at  very  nearly  the  same  results  using  the  ophthalmometer  of 
Helmholtz.  —  Still  more  accurate  results  may  be  obtained  by  using  trans- 
lucent mires  which  are  illuminated  from  behind  by  electric  lamps.  In 
these  conditions  an  experienced  observer  can  almost  guarantee  exact- 
ness to  a  tenth  of  a  dioptry  or  thereabouts. 

30.  Results  of  the  Measurement  of  the  Cornea.  —  The  radius  of  the 
cornea  (at  the  summit)  varies  between  7  and  8.5  mm.  It  is  extremely  rare 
to  find  a  cornea  the  radius  of  which  is  not  situated  between  these  limits, 
except  in  cases  of  keratoconus. 

The  curve  (fig.  41)  shows  the  distribution  of  the  different  curvatures 
in  a  certain  number  of  men  (emmetropes)  whom  I  examined  in  collabo- 


OPHTHALMOMETRY 


55 


ration  with  Dr.  Bourgeois.  The  average  was  43.1  D  =  7.8  mm.  It  is 
noticeable,  however,  that  these  same  measurements  show  that  the  radius 
is  greater  in  persons  tall  in  stature  and  with  a  large  cranial  circumfer- 
ence, (i)  Now  the  persons  whom  we  examined  were  indeed  of  tall 
stature  (cuirassiers).  It  may  be,  therefore,  that  the  average  length  of 
the  radius  may  be  slightly  smaller  than  that  which  I  have  just  indicated. 
—  It  would  be  an  error  to  think  that  one  radius  rather  than  another 
corresponds  with  emmetropia.  As  Javal  says  an  elephant  and  a  mouse 
may  both  be  emmetropic  despite  the  fact  that  their  corneal  radii 
must  necessarily  be  very  different.  —  It  seems  that  we  can  express  the 


35 
30 
25 
20 
15- 
10- 
5- 


7.17      7.33      7.49       7.66      7.81       8.02      8.23      8.43mm 

Fig.  41.  —  The  abscissas  indicate  the  radii  of  curvature  of  the  cornea  in  millimeters, 
he  ordinates  the  number  per  hundred  of  emmetropes  in  whom  we  meet  the  radius  of  curva- 
ture in  question. 

relation  by  saying  that  in  the  emmetropic  eye  there  exists  a  constant 
relation  between  the  radius  of  curvature  of  the  cornea  and  the  length 
of  the  ocular  axis,  so  that  the  ocular  shell  of  different  emmetropic  eyes 
would  always  be  a  reproduction  of  the  same  type,  a  little  enlarged  or  a 
little  diminished.  —  The  existence  of  the  myopia  and  hypermetropia  of 
curvature  (corneal)  is  not  yet  demonstrated  (2)  except,  perhaps,  for 
certain  cases  of  very  high  hypermetropia  which  approach  microphthal- 
mia ;  but  their  existence  is  beyond  doubt. 

If  I  except  cases  of  astigmatism,  different  in  both  eyes,  it  is  very  rare 
to  find  a  difference,  ever  so  slightly  noticeable,  between  the  corneal  re- 

(1)  Steiger  has  since  found  a  still  more  manifest  relation  between  the  radii  of  the  corneas  and  the 
distance  between  the  eyes. 

(2)  See,  however,  the  communication  of  Sulzer  to  the  Congress  of  the  French  Society  of  Ophthal- 
mology, 1896. 


56  PHYSIOLOGIC  OPTICS 

fraction  of  the  two  eyes  of  the  same  person,  even  in  cases  of  anisome- 
tropia.  Amongst  the  cuirassiers  mentioned  above  there  were  not  more 
than  two  per  cent,  who  showed  a  difference  exceeding  a  half  dioptry 
between  the  two  eyes. 

EXAMINATION  OF  THE  PERIPHERAL  PART  OF  THE  CORNEA.  —  Up  to 
the  time  when  Javal  and  Schioetz  made  a  clinical  method  of  ophthal- 
mometry  there  was  little  known  of  the  form  of  the  cornea.  The  ophthal- 
mometer-of  Helmholtz  being  too  complicated  to  make  many  measure- 
ments, one  was  limited  to  measuring  three  points  of  a  meridian,  that 
which  corresponds  to  the  visual  line  and  another  at  some  distance  on 
either  side.  As  the  peripheral  radii  were  found  to  be  greater  than  the 
central  radius,  and  as,  in  consequence,  the  cornea  could  not  be  consid- 
ered as  a  sphere,  the  curvature  of  the  second  degree  which  approached 
nearest  the  meridian  measured  was  calculated  (see  fig.  42).  Thus  it  was 
that  the  idea  was  disseminated  that  the  form  of  the  cornea  (non-astig- 
matic) would  be  that  of  an  ellipsoid  of  revolution  around  the  long  axis, 
which  axis  would  be  directed  outwards  from  the  visual  line  and  form 
an  angle  of  about  5°  («)  with  this  line.  This  idea  differs  widely  from 
the  reality;  the  cornea  does  not  resemble  an  ellipsoid.  Helmholtz  in- 
sisted from  the  start  on  the  fallacy  of  the  comparison. 

After  the  construction  of  modern  ophthalmometers  it  became  much 
easier  to  study  this  question.  The  second  model  of  the  Javal  and 
Schioetz  ophthalmometer  is  provided  with  a  very  large  keratoscopic  disc 
divided  into  graduations  of  5°  by  concentric  rings.  After  having  made  the 
usual  measurements,  during  which  time  the  patient  looks  at  the  center 
of  the  objective,  the  measurement  is  repeated  making  him  look  5°  to 
the  left,  10°  to  the  left,  etc. ;  and,  after  having  thus  measured  the  right 
half  of  the  horizontal  meridian  we  measure  the  left  half.  We  repeat  the 
measurements  for  the  vertical  meridian.  —  Measurements  of  this  kind 
have  been  made  in  Paris  by  Sulzer  and  Eriksen  (fig.  42) ;  these  measure- 
ments confirmed  the  assertion  of  Aubert  and  Matthiesen  who,  using  the 
ophthalmometer  of  Helmholtz,  had  said  that  the  cornea  could  be  divided 
into  two  parts,  a  central  one,  which  is  approximately  spherical  and  which 
we  call  the  optic  part,  and  a  peripheral  one  or  basilar  part,  which  is  much 
flattened.  Eriksen  reckoned  as  belonging  to  the  optic  part  that  part 
the  refraction  of  which  does  not  differ  more  than  one  dioptry  from  the 
central  refraction.  Its  extent  varies  a  little  in  different  eyes.  Follow- 
ing are  the  limits  of  the  optic  part  compared  with  those  of  the  entire 
cornea,  after  Eriksen: 


OPETHALMOMETRT 


57 


Optic  Part. 

Outwards 16.5° 

Inwards , 14° 

Above 12.5° 

Below..  13.5° 


Cornea. 
44.7° 
40.1° 
38.5° 
42.2° 


The  figures  are  the  averages  of  measurements  made  on  24  eyes. 
The  total  width  of  the  cornea  is,  therefore,  not  much  less  than  90°, 
and  that  of  the  optic  part  is  about  30°,  or  a  third  of  the  entire  width. 


30 


2S 


30" 


0°         <l     0°  10° 

Visual  I«ine 


Na 


Fig.  42.  —  Diagram  of  corneal  refraction  after  Eriksen.  —  The  abscissas  indicate  the  di§- 
tance  of  the  visual  line  in  degrees,  the  ordinates,  the  corneal  refraction  in  dioptrics. 

The  full  curve  indicates  the  refraction  of  the  horizontal  meridian  of  a  left  cornea  measured 
in  graduations  of  five  degrees.  The  zero  corresponds  to  the  visual  line.  —  aa,  optic 
part  of  the  cornea ;  06,  06,  basilar  part.  —  The  dotted  curve  cc  corresponds  to  the  ellip- 
soid calculated  according  to  the  three  measurements  taken  at  0°  and  25°  on  the  right 
and  left  of  the  visual  line ;  dd  is  the  axis  of  this  ellipsoid  and  the  distance  of  this  line 
from  zero  corresponds  to  the  angle  which  is  often  called  the  angle  a.  —  We  see  that  the 
true  form  of  the  cornea  differs  considerably  from  the  ellipsoid. 

The  horizontal  diameter,  as  well  that  of  the  optic  part  as  that  of  the 
entire  cornea,  is  a  little  greater  than  the  vertical  diameter. 

Neither  Sulzer  nor  Eriksen  have  found  an  axis  of  symmetry  properly 
so  called.  Nevertheless,  most  of  the  diagrams  of  the  latter  show  a 
tendency  to  symmetry  around  an  axis  directed  about  5°  outwards  and 


58  PHYSIOLOGIC  OPTICS 

a  little  below  the  visual  line.  If,  therefore,  the  comparison  with  an 
ellipsoid  is  persisted  in,  we  must  imagine  it  much  more  pointed  than  we 
have  done  up  to  the  present,  and  we  must  suppose  the  summit  cut-off 
by  a  section  perpendicular  to  the  axis  and  replaced  by  a  spherical  cap. 

As  far  as  the  optics  of  the  eye  are  concerned,  the  obliquity  of  the 
cornea  plays  only  a  slightly  important  role,  since  the  optic  part  of  the 
cornea  is  nearly  spherical.  This  part  corresponds  to  a  linear  diameter  of 
about  4  mm.  When  the  pupil  is  large  the  basilar  part  may,  therefore, 
play  a  certain  part ;  according  to  the  little  table  of  Eriksen  it  would  be 
especially  inwards  and  above  that  its  influence  would  be  felt.  But  it  is 
impossible  to  know  anything  of  it  without  having  examined  each  eye 
by  itself,  for  the  obliquity  of  the  cornea  is  often  compensated  for  by 
the  eccentricity  of  the  pupil.  The  position  of  the  pupil  varies  much  in 
different  eyes.  Sulzer  found  that  on  an  average  the  center  of  the  pupil 
is  5°  outwards  from  the  visual  line,  and  that  it  is  sometimes  displaced 
upwards,  sometimes  downwards.  This  decentering  of  the  pupil  may, 
therefore,  compensate  for  the  obliquity  of  the  cornea,  so  that  it  is  espe- 
cially outwards  that  we  must  expect  to  notice  the  effect  of  the  peripheral 
flattening. 

The  basilar  portion  is  less  regular  and  much  less  polished  than  the 
central  portion,  which  partly  explains  the  slight  success  of  optic  iridec- 
tomies.  The  catoptric  images  have  frequently  a  diffuse  aspect  and  the 
ophthalmometric  measurements  leave  much  to  be  desired.  Eriksen  also 
has  tried  to  obtain  an  idea  of  the  variation  of  the  radius  of  the  peripheral 
parts  by  examining  the  form  which  the  image  of  a  white  square  assumes 
in  the  horizontal  meridian,  at  different  distances  from  the  visual  line. 

We  see  on  fig.  43  that  the  image  becomes  longer  and  longer  until 
about  30°  from  the  visual  line,  where  it  is  two  and  a  half  times  greater 
than  at  the  center.  Just  at  the  periphery  the  image  becomes  narrower, 


•Fig.  43.  —  Forms  of  the  image  of  a  white  square  at  different  parts  of  the  cornea  (horizontal 
..«^meridian,  internal  half),  after  Eriksen.  —  The  figures  at  the  top  of  the  squares  indicate 

the  distance  in  degrees  from  the  visual  line ;  those  at  the  bottom  the  refraction  (in  the 

horizontal  meridian)  in  dioptrics. 

and  ends  as  a  rectangle  placed  upright ;  at  this  place  the  image  is  some- 
times double;  a  second  image  is  formed  still  farther  away  on  the  edge 


OPHTHALMOMETRY  59 

towards  the  sclera,  and  this  image  is  inverted  in  the  horizontal  direc- 
tion, but  not  in  the  opposite  direction.  These  latter  phenomena  indicate 
that  the  curvature  increases  very  considerably  towards  the  border,  and 
that  beyond  this  place  there  is,  at  least  in  some  eyes,  a  concavity,  like 
a  furrow  which  separates  the  cornea  from  the  sclera.  We  must  note 
that  the  images  should  increase  a  little  in  height  towards  the  periphery 
at  the  same  time  that  they  increase  in  width,  because  the  curvature 
diminishes  also  in  the  vertical,  but  much  less  than  in  the  horizontal  direc- 
tion. This  increase  is  not  indicated  on  the  figure. 

In  a  general  way  we  may,  therefore,  consider  the  portion  of  the  cornea 
which  plays  a  part  in  the  optics  of  the  eye  as  spherical,  so  that  the  angle 
«,  understood  in  the  sense  in  which  we  generally  accept  it,  loses  its 
importance.  —  This  is  why  I  have  defined  the  angle  «  as  being  the 
angle  between  the  visual  line  and  the  optic  axis  of  the  eye,  a  definition 
which  others  have  also  given  to  it. 

Note,  furthermore,  that  the  normal  cornea  is  slightly  astigmatic ;  we 
reserve  a  special  chapter  for  this  anomaly  of  refraction. 

The  radius  of  the  normal  cornea  does  not  fall  below  7  mm.,  but  in 
cases  of  keratoconus  we  may  meet  radii  of  6  or  5  mm.,  or  even  still 
smaller  radii,  to  a  point  where  the  arc  of  the  ophthalmometer  becomes 
too  short;  we  cannot  separate  the  mires  sufficiently  to  obtain  contact. 
The  images  of  the  mires  assume  in  this  case,  as  also  when  there  are 
corneal  opacities,  irregular  forms. 

By  the  Sulzer-Eriksen  method  we  determine  the  radius  of  curvature 
at  a  given  part  of  the  cornea.  We  obtain  by  this  method  a  very  good 
idea  of  the  form  of  the  cornea,  but  the  results  are  not  directly  applicable 
to  ocular  dioptrics  for  the  reasons  given  on  page  13.  To  be  able  to 
calculate  the  aberration  produced  by  a  peripheral  flattening  of  the 
cornea,  we  should  know  the  normal  (the  part  of  the  perpendicular  to 
the  cornea  comprised  between  the  latter  and  the  visual  line).  To  deter- 
mine it  Brudzewski  made  certain  changes  in  the  ophthalmometer.  He 
replaced  the  arc  by  a  larger  one,  reaching  170°.  One  of  the  mires  is 
fixed  at  the  middle  of  the  arc  so  that  its  border  when  prolonged  would 
pass  through  the  axis  of  the  telescope,  while  the  other  mire  slides  on  the 
arc  so  as  to  be  able  to  obtain  contact.  The  observed  person  fixes  the 
middle  of  the  objective  during  all  the  measurements.  He  uses  prisms 
of  different  doubling  power.  He  begins,  for  example,  with  a  prism 
doubling  I  mm. ;  and,  the  arc  being  placed  horizontally,  he  determines 
the  position,  on  the  nasal  side,  which  the  movable  mire  must  have  so 
that  he  may  obtain  contact.  He  then  makes  the  same  determination 


60 


PHYSIOLOGIC   OPTICS 


on  the  temporal  side,  after  having  placed  the  arc  vertically  upwards  and 
downwards.  These  measurements  give  the  length  of  the  normals  to 
the  cornea  at  four  places,  situated  at  I  mm.  from  the  visual  line.  He 
then  replaces  the  prism  by  another  doubling  2  mm.,  and  so  forth.  Know- 
ing the  normal  he  can  then  directly  calculate  the  aberration  produced 
by  the  corresponding  part  of  the  cornea  (see  chapter  VII). 

We  observe,  furthermore,  that  the  ophthalmometer  lends  itself  very 
well  to  the  examination  of  the  curvature  of  the  surfaces  of  the  dead  eye. 
Holth  thus  made  a  series  of  measurements  in  the  laboratory  of  the  Sor- 
bonne.  He  placed  the  eye  with  the  cornea  upwards  under  a  mirror  at  45° 
which  sent  the  reflected  image  in  the  direction  of  the  ophthalmometer. 
The  mirror  must  not  be  too  small,  for  it  must  allow  us  to  measure  also 
the  peripheral  parts  of  the  surfaces  by  displacing  the  instrument.  As  the 
surfaces  are  generally  more  or  less  misty,  we  are  obliged  to  coat  them 


Fig.  44.  —  Keratoscopic  images  of  a  cornea  presenting  a  considera1  le  astigmatism  at  the 
central  part  (central  ring  of  figure  C),  while  the  remainder  of  the  cornea  is  nearly 
exempt  from  it.  After  Javal.  —  C,  direct  look ;  H,  upwards  look  ;  B,  downwards;  D,. 
to  the  right ;  G,  to  the  left. 

with  a  very  thin  layer  of  oil  to  make  them  bright.  It  was  necessary 
for  the  measurement  of  the  cornea  to  make  an  injection  into  the  vitreous 
body  so  as  to  make  its  tension  that  of  the  eye,  but  it  was  interesting 
to  note  how  much  he  could  change  the  tension  of  the  eye  without 
observing  any  perceptible  alteration  in  the  curvature  of  the  cornea. 


01*11  TUALMOMETRY 


61 


To  measure  the  curvature  of  the  posterior  surface  of  the  cornea,  Holth 
injected  a  solution  of  gelatine  into  the  anterior  chamber;  as  soon  as 
the  gelatine  solidified  he  removed  the  cornea  and  measured  the  anterior 
surface  of  the  cast,  made  bright  with  oil.  The  anterior  surface  of  the 
crystalline  lens  is  measured  directly,  after  the  cornea  and  iris  have  been 
removed.  To  measure  the  posterior  surface  he  cut  the  eye  in  two, 
along  the  equator,  and,  the  vitreous  body  being  removed,  the  ey;e  was 
placed  with  the  cornea  downwards.  Holth  gave  an  account  of  the  results 
achieved  by  him  at  the  Ophthalmological  Congress  of  Utrecht  in  1899 
(see  also  page  182). 

EXAMINATION  WITH  THE  KERATOSCOPIC  Disc. — The  measurement  of 
peripheral  parts  of  the  cornea  takes  too  much  time  to  be  of  service  in 


Fig.  45.  —  Keratoscopic  figures  of  a  case  analogous  to  that  of  figure  44.  After  Javal. 

clinics,  but  we  can  obtain  information  about  the  peripheral  parts  of  the 
cornea  by  means  of  the  keratoscopic  disc,  a  circular  disc,  on  which  are 
painted  concentric  circles  of  different  colors.  We  can  place  it  on  the 
telescope  of  the  ophthalmometer  by  taking  out  the  double  refracting 
prism,  or  simply  by  holding  it  in  the  hand  and  looking  through  a  central 
aperture  (Placido).  Generally  the  patient  looks  towards  the  middle  of 
the  disc ;  the  images  of  the  circles  are  then  circular  in  a  normal  eye,  and 
elongated  along  the  meridian  of  least  refraction  in  the  astigmatic  eye; 


62  PHYSIOLOGIC  OPTICS 

by  making  the  patient  look  towards  the  border  of  the  disc  it  is  easy 
to  establish  the  peripheral  flattening  of  the  cornea. 

In  cases  of  irregular  astigmatism  the  circles  assume  irregular  forms ; 
and  we  may  often,  by  studying  these  forms,  obtain  important  informa- 
tion on  the  anomaly  in  question.  —  Thus  figs.  44  and  45  show  the 
appearance  of  the  disc  in  cases  in  which  the  central  part  of  the  cornea 
was  affected  with  a  pronounced  astigmatism,  while  the  middle  zones 
were  scarcely  affected  at  all;  we  see,  in  fact,  that  the  central  ring  of 


Fig.  46.  —  Keratoscopic  figures  of  a  case  of  keratoconus.  After  Javcd. 

figure  C,  which  corresponds  to  the  middle  of  the  cornea,  is  much 
lengthened,  while  the  more  peripheral  rings  are  almost  circular.  —  In 
cases  of  keratoconus  the  image  of  the  disc  is  very  small  when  it  is 
formed  at  the  summit  of  the  cornea,  but  the  least  deviation  of  the  look 
causes  a  change  of  form  by  lengthening  it  in  the  radial  direction  (fig.  46). 
We  have  seen  (page  36)  that  the  visual  line  passes  through  the  cornea 
perpendicularly  or  nearly  so.  When  making  a  keratoscopic  examina- 
tion the  observed  person  looks  into  the  telescope;  the  center  of  the 
concentric  rings  of  the  image  indicates,  therefore,  the  place  where  the 
visual  line  passes  through  the  cornea,  and  if,  at  the  same  time,  we 
illuminate  the  eye  moderately  we  can  account  for  the  direction  of  the 


OPHTHALMOMETR7 


visual  line  relatively  to  the  different  parts  of  the  eye.    It  may  be  useful 
to  modify  the  appearance  of  the  disc.  Figure  460  shows  the  keratoscopic 
rr  appearance  of  an  eye  affected 

with  a  high  degree  of  astig- 
matism, and  of  which  the 
angle  «  has  an  unusual  size; 
the  small  black  circle  indi- 
cates the  pupil,  the  white  fig- 
ure is  the  cornea!  image  of 
a  large  white  disc  provided 
with  a  black  cross,  the  arms 
of  which  were  placed  in  the 
principal  meridians;  its  el- 
liptical form  is  due  to  the 
astigmatism.  The  visual  line 
corresponds  to  the  intersec- 
tion of  the  two  black  lines. 
We  notice  that  it  is  placed 
very  eccentrically  in  the  pupil  so  that  the  four  quadrants  of  the  latter 
are  of  very  different  size.  The  angle  «  was  about  9°;  the  axis  of  the 
crystalline  lens  was  directed  8.8°  outwards  and  3.8°  downwards  from 
the  visual  line. 

As  in  every  instance  in  which  the  angle  a  has  an  unusual  size,  the 
cause  was  to  be  found  in  the  displacement  of  the  fovea,  a  displacement 
which,  in  this  case,  manifests  itself  also  by  an  increased  distance  between 
the  point  of  fixation  and  the  blind  spot  (fig.  466).  The  internal  border  of 
the  latter  was  at  15°  instead  of  11°  or  12°. 


Fig.  46a.  —  Keratoscopic  image  of  an  eye  with  a 
large  angle  a. 


Fig.  466.  —  Spot  of  Mariotte  of  an  eye  with  a  large  angle  a,  compared  with  that  (dotted) 
of  a  normal  eye.    a,  point  of  fixation. 

31.  Measurement  of  the  Angle  a.  —  For  the  following  measurements 
I  use  the  ophthalmophakometer  (fig.  47,  see  page  44).  I  designate  by  A 
the  cursor  which  carries  only  one  lamp;  by  B  that  which  carries  two, 
placed  on  the  same  vertical  rod,  and  by  C  the  third  cursor  which  carries 
a  rod  on  which  moves  a  small  bright  ball  which  serves  as  the  point  of 
fixation. 

I  place  the  arc  horizontally  and  the  cursor  B  at  the  zero  of  the 


64 


PHYSIOLOGIC  OPTICS 


graduation  of  the  arc  (i)  so  that  its  two  lamps  are  in  the  same  vertical 
plane  as  the  middle  of  the  objective  of  the  telescope,  and  I  request  the 


Fig.  47.  —  The  ophthalmophakometer. 


Fig.  48.  —  The  images  of  Purkinje  observed  with  the  ophthalmophakometer.    The  two 
lamps  B,  figure  47,  are  in  the  same  vertical  plane  as  the  axis  of  the  telescope  and  the 
observed  person  looks  at  5.7°  on  the  nasal  side,  so  as  to  align  the  images.     The  optic 
axis  of  the  eye  coincides  in  these  circumstances  with  the  axis  of  the  telescope. 
(1)  The  lamp  of  the  cursor  A  is  not  used  in  this  experiment. 


OPHTHALMOMETRY 


observed  person  to  look  towards  this  latter  place.  It  is  clear  that,  if 
the  surfaces  of  the  eye  were  centered  around  the  visual  line,  we  should, 
in  these  circumstances,  see  the  six  images  of  reflection  on  the  same 


Fig.  49.  —  Position  of  the  images  when  the  observed  person  looks  into  the  telescope.    Th 
position  of  the  lamps  is  the  same  as  in  figure  48.  At  the  middle,  the  corneal  images 
on  the  right,  those  of  the  anterior  surface  of  the  crystalline  lens;  on  the  left,  those  of 
the  posterior  surface  of  the  crystalline  lens.  The  images  of  the  posterior  surface  of  the 
cornea  are  not  visible. 


Fig.  50.  —  The  two  lamps  are  in  the  same  horizontal  plane  as  the  axis  of  the  telescope. 
The  observed  person  looks  into  the  telescope. 

vertical  line  (fig.  48)  (those  of  the  posterior  surface  of  the  cornea  are 
not  visible  under  these  conditions).  But  this  has  never  happened. 


66 


PHYSIOLOGIC   OPTICS 


We  always  see,  as  in  fig.  49,  the  images  of  the  anterior  surface  of  the 
crystalline  lens,  on  the  one  side,  those  of  the  posterior  surface  of  the 
crystalline  on  the  other,  and  the  corneal  images  in  the  middle.  I  then 
request  the  observed  person  to  fix  the  bright  ball  of  the  cursor  C,  and 
I  displace  this  cursor  until  I  see  the  images  placed  as  in  fig.  48.  The 
optic  axis  of  the  eye  is  then  in  the  vertical  plane,  passing  through  the 
axis  of  the  telescope,  and  the  angular  distance  of  the  cursor  C  from 
the  telescope  indicates  how  much  the  visual  line  deviates  from  the  optic 
axis  in  the  horizontal  plane.  —  We  find  that  it  is  necessary  to  place  the 
cursor  C  on  the  nasal  side  at  a  distance  from  the  telescope  varying 
between  4°  and  7°  (angle  «).  —  This  angle  can  be  determined  with  very 
great  exactness. 


Fig.  51.  —  Defect  of  centering;  it  is  impossible  to  align  the  six  images. 


I  then  place  the  arc  vertically  so  that  the  two  lamps  are  in  a  horizontal 
plane :  generally  the  six  images  are  not  on  a  horizontal  line  (fig.  50) ; 
by  displacing  the  cursor  C,  which  the  observed  person  fixes,  until  I  see 
all  the  images  on  a  horizontal  line,  I  determine  the  vertical  deviation 
of  the  visual  line. 

The  optic  axis  is  nearly  always  directed  outwards  from  the  visual 
line,  and  most  frequently  downwards  (2°  to  3°);  sometimes  we  find  it, 
however,  in  the  same  horizontal  plane,  or  deviated  a  little  upwards. 

DEFECT  OF  CENTERING.  —  We  sometimes  observe  that  it  is  not  pos- 
sible to  place  the  six  images  on  a  straight  line  (fig.  51).  We  succeed  in 
aligning  two  pairs,  whichever  we  want,  but  the  third  remains  outside.  This 


OPHTHALMOMETRY  67 

takes  place  when  the  eye  is  not  exactly  centered;  that  is  to  say,  when 
the  axis  of  the  crystalline  lens  does  not  pass  through  the  center  of 
curvature  of  the  cornea  (the  posterior  surface  of  which  I  neglect).  We 
can  nearly  always  establish  slight  defects  of  this  kind,  but  most  fre- 
quently they  are  negligible.  When  we  find  more  considerable  defects, 
it  is  generally  because  the  axis  of  the  crystalline  lens  passes  a  little  (up 
to  0.25  mm.)  above  the  center  of  curvature  of  the  cornea. 

32.  Determination  of  the  Position  of  the  Internal  Surfaces.  —  To  meas- 
ure the  radii  of  the  surfaces  we  must  determine:  i°  the  position  (the 
distance  from  the  summit  of  the  cornea)  of  the  surfaces ;  2°  the  position 
of  the  centers.  It  is  true  that  there  exists,  as  we  shall  see,  a  means  of 
determining  the  radii  directly,  but  we  must  not  forget  that  all  the  sizes 
which  we  are  measuring  here  are  apparent  sizes,  and  that,  to  find  the  real 
values,  we  must  reduce  the  results  by  a  calculation  following  the  rules 
which  we  have  already  given  (page  41).  To  make  this  reduction  it  is 
necessary  to  know  the  position  of  the  surfaces,  which  knowledge  is 
likewise  necessary  in  order  that  we  may  be  able  to  combine  the  sur- 
faces with  one  another  so  that  we  may  proceed  to  calculate  the  entire 
optic  system. 

I  take  the  anterior  surface  of  the  crystalline  lens,  as  an  example,  and 
I  suppose  that  we  are  making  the  measurement  in  the  horizontal  direc- 
tion. It  is  useful  to  dilate  the  pupil. 

I  place  the  arc  of  the  instrument  horizontally,  and  I  place  also,  as  far 
away  as  possible  from  the  telescope  the  cursor  A,  the  lamp  of  which 
must  be  sufficiently  brilliant  that  the  image  of  the  surface  to  be  meas- 
ured may  be  quite  visible.  This  done,  I  place  the  cursor  C,  which  carries 
the  mark  of  fixation,  at  a  place  such  that  the  optic  axis  of  the  eye  may 
bisect  the  angular  distance  between  the  telescope  and  A  (i).  It  is 
necessary,  therefore,  to  have  previously  measured  the  angle  «.  We 
then  displace  the  cursor  B,  the  lamps  of  which  must  be  very  feeble  so 
that  we  may  see  only  the  corneal  images,  until  the  crystalline  image  of 
A  is  exactly  on  the  same  vertical  as  the  corneal  images  of  B.  Glancing 
at  fig.  52,  it  is  easy  to  see  that  we  now  possess  the  elements  necessary 
to  calculate  the  distance  of  the  anterior  surface  of  the  crystalline  lens 
from  the  summit  of  the  cornea,  for  the  angle  c  is  half  the  angular  distance 
of  A  from  the  telescope,  and  the  angle  d  is  half  of  the  angular  distance 

(1)  If  the  eye  is  not  centered  we  must  replace  the  optic  axis  by  the  line  passing  through  the  center 
of  curvature  of  the  cornea  and  the  center  of  the  surface  which  we  desire  to  measure.  We  find  this  line 
as  we  found  the  optic  axis  in  the  preceding  experiment,  by  aligning  the  corneal  images  with  the  images 
of  the  surface  to  be  measured. 


68  PHYSIOLOGIC  OPTICS 

(i)  of  B  from  the  telescope.    Supposing  that  we  knew  the  radius  of  the 
cornea  R±,  which  should  have  been  measured  previously,  the  triangle 


Fig.  52.  —  Method  of  determining  the  position  of  an  internal  surface  of  the  eye.  —  S1}  an- 
terior surface  of  the  cornea ;  Clt  its  center ;  S2,  anterior  surface  of  the  crystalline  lens  ; 
C2,  its  center;  Cj,  C2,  optic  axis  of  the  eye. 

O2  C±  P  gives  us  the  relation  O2  Cx  =  R3    -JlJ-f ,  and  we  have  for  the 
distance,  looked  for 

r»  n         T?          n  P         P    (-(        sin  d\        TJ    sip  c  —  sin  d 

O,  O.,  =  K,  —  Oo  C/i  =  K!   II : I   =  K,    : . 

\          sin  c/  sm  c 

If  very  great  exactness  is  not  desired,  the  sines  can  be  replaced  by 
the  arcs. 

EXAMPLE.  —  Let  the  radius  of  the  cornea  be  7.98  mm.,  the  distance 
of  A  from  the  telescope  28°  nasal,  that  of  B  16.8°  nasal;  we  will  have 
Oi  O2  =  7-98  (i  —  ?i°8u°'  )  =  3.16  mm.  The  apparent  depth  of  the 
anterior  chamber  would,  therefore,  be  3.16  mm.,  whence  we  find  the  true 
value  3.73  mm.  by  placing  in  the  formula  -^-  -f  -§-  =  I,  the  values  Fx  = 
23.64,  F2  =  31.61,  fx  =  — •  3-16. 

33.  Determination  of  the  Centers  of  the  Internal  Surfaces.  —  We  place 
A  above  the  telescope,  and  we  move  C  with  the  mark  of  fixation  as  far 
as  possible  from  the  telescope,  but  so  that  the  image  may  not  disappear 

(1)  We  can  imagine  the  two  lamps  of  B  united  into  one  only,  at  the  level  of  the  lamp  of  A. 


OPHTHALMOMETR7 


69 


behind  the  iris  ;  then  we  displace  B  until  the  corneal  images  of  its  two 
lamps  are  on  the  same  vertical  line  as  the  crystalline  image  of  A. 

Under  these  conditions,  the  axis  of  the  telescope  is  perpendicular  to 
the  apparent  anterior  surface  of  the  crystalline  lens  (i).  We  find  the  angle 


Fig.  53.  —  Method  of  determining  the  position  of  an  internal  surface  of  the  eye.    The 
letters  signify  the  eame  as  in  figure  52. 

a  (fig.  53)  by  adding  (subtracting)  the  angle  x  to  the  angular  distance 
of  C  from  the  telescope.  The  angle  b  is  half  of  the  distance  of  B  from 
the  telescope ;  we  have  C2  Q  =  R!  -|{J-|  and  the  distance  sought  equal  to 


sin  a  -{-  sin  6 
sin  a 


EXAMPLE  —  In  the  same  eye  as  before  let  «  =  5.1°,  the  distance  of  B 
from  the  telescope  12.4°  temporal  and  that  of  C  from  the  telescope  9.9° 
nasal.  We  would  then  have  for  the  distance  sought  7.98  (i  +  ;£  "°  )  = 
18.28  mm.  and  the  apparent  radius  would  be  18.28  mm.  —  3.16  mm.  = 


(1)  If  we  imagine  the  lamp  placed  at  the  center  of  the  objective,  the  ray  which  reaches  the  observer's 
eye  would  be  reflected  exactly  on  itself,  which  can  take  place  only  if  it  meets  perpendicularly  the  ap- 
parent surface. 


70  PHYSIOLOGIC  OPTICS 

15.12  mm.    The  position  of  the  real  center  would  be  13.78  mm.  (i)  and 
the  radius  of  the  real  surface  13.78  mm.  —  3.73  =  10.05  mm- 

34.  Direct  Determination  of  the  Radii.  —  In  fig.  49,  as  well  as  in  figs. 
50  and  51,  the  ratio  between  the  distances  separating  the  two  images 
of  the  same  kind  is  equal  to  the  ratio  between  the  apparent  radii.  We 
may,  indeed,  consider  the  distance,  separating  the  two  lamps  as  an  object, 
three  images  of  which  are  formed  on  the  pupil;  these  images  are  pro- 
portional to  the  radii  following  the  formula  -J-  =  -£- ,  since  O  and  /  are 
the  same  in  the  three  cases. 

We  can  make  sufficiently  accurate  measurements  of  the  radii  if  we 
make  use  of  two  cursors  similar  to  A  and  two  others  similar  to  B.  We 
place  the  lamps  A  in  such  a  position  as  to  be  able  to  observe  clearly 
the  images  produced  by  the  anterior  surface  of  the  crystalline  lens. 
Then  we  displace  the  cursors  B,  the  lamps  of  which  must  be  feeble, 
until  the  corneal  images  of  the  lamps  of  each  are  on  the  same  straight 
line  as  one  of  the  crystalline  images  of  A.  We  consider  the  distance 
which  separates  the  cursors  A  as  object  for  the  anterior  surface  of  the 
crystalline  lens,  and  that  separating  the  cursors  B  as  object  for  the 
cornea.  As  the  images  are  alike,  the  radii  must  be  inversely  propor- 
tional to  the  objects.  Knowing  the  radius  of  the  cornea,  we  can,  there- 
fore, calculate  the  apparent  radius  of  the  anterior  surface  of  the  crys- 
talline. 

To  determine  the  astigmatism  of  the  surface  we  must  repeat  all  the 
measurements  in  the  vertical  meridian. 

The  posterior  surface  of  the  crystalline  lens  is  measured  exactly  like 
the  anterior  surface.  As  to  the  posterior  surface  of  the  cornea,  its 
image  is  not  visible  at  the  middle  of  the  pupil.  We  must,  therefore,  limit 
ourselves  to  measuring  the  peripheral  parts.  The  direct  determination 
of  the  position  of  the  surface,  following  the  method  indicated  in  para- 
graph 32,  is  not  applicable  for  the  same  reason,  but  the  position  of  the 
center  can  be  determined  after  paragraph  33,  and  the  length  of  the 
radius  as  we  have  just  explained,  which  gives  indirectly  the  thickness 
of  the  cornea.  It  is  necessary  to  have  previously  measured  the  radius 
of  the  anterior  surface  of  the  cornea  at  the  place  where  we  are  making 
the  measurement,  for  generally  this  place  is  so  peripheral  that  the 
flattening  of  the  cornea  makes  itself  felt.  Besides,  the  posterior  sur- 


(1)  [Considering  that  we  have  again  obtained  this  apparent  position  with  reference  to  the  refraction 
of  the  cornea,  -we  must  therefore  in  the  formula  -*X  -j-  *X  =-  1  put  FI  =  23.64;  F2  =  31.61  and 
fl  _  _  18.28,  this  gives /2  =  13.78.]— W. 


OPHTHALMOMETRY  71 

face  undergoes,  towards  the  periphery,  a  flattening  analogous  to  that 
of  the  anterior  surface,  so  that  the  relation  between  the  radii  of  the 
two  surfaces  seems  almost  the  same  everywhere. 

35.  General  Remarks.  —  We  can,  therefore,  thus  measure  on  the  living 
subject  all  the  optic  constants  except  the  indices.  But  we  must  not 
deceive  ourselves  as  to  the  exactness  of  these  measurements;  except- 
ing those  of  the  anterior  surface  of  the  cornea,  they  are  not  very  exact. 
In  fact,  the  crystalline  images  are  feeble,  and  those  of  the  anterior  sur- 
face of  the  crystalline  lens  very  diffuse,  which  causes  the  measurement 
to  become  less  certain;  there  are  also  other  sources  of  errors,  such  as 
that  made  by  comparing  the  surfaces  to  spherical  surfaces.  It  may 
happen  also  that  the  observed  eye  does  not  fix  exactly  at  the  moment 
of  observation.  When  we  wish  to  determine,  for  example,  the  radius 
of  the  anterior  surface  of  the  crystalline  lens,  we  have  to  depend  on 
three  measurements,  that  of  the  radius  of  the  anterior  surface  of  the 
cornea,  that  of  the  position  of  the  anterior  surface  of  the  crystalline, 
and  that  of  the  position  of  its  center.  The  errors  of  these  measure- 
ments are  added  in  the  final  result.  I  do  not  think,  therefore,  that  we 
can  guarantee  an  exactness  of  more  than  half  a  millimeter  in  the  final 
result.  As  far  as  the  optics  of  the  eye  are  concerned,  this  want  of 
exactness  does  not  present  any  considerable  importance.  Indeed,  it 
must  not  be  forgotten  that  the  difference  of  index  of  the  media  which 
separate  the  internal  surfaces  is  very  slight,  making  it  unnecessary  to 
know  the  radii  very  exactly ;  an  error  of  half  a  millimeter  in  the  measure- 
ment of  the  anterior  surface  of  the  cornea  corresponds  to  about  3  D., 
whilst  the  same  error  in  the  measurement  of  the  anterior  surface  of  the 
crystalline  lens  corresponds  only  to  a  third  of  a  dioptry.  —  But,  as  to 
the  thickness  of  the  crystalline  lens,  which  is  only  4  mm.,  an  error  of 
half  a  millimeter  presents  a  vast  importance.  The  much  disputed  ques- 
tion of  knowing  whether  the  crystalline  lens  changes  its  thickness 
during  accommodation  can  with  difficulty  be  decided  by  the  observation 
of  the  crystalline  images,  for  the  alleged  change  (an  increase  of  0.4  mm.) 
does  not  exceed  the  limit  of  error. 

Ophthalmometry  of  the  cornea  has  passed  the  doors  of  the  labora- 
tories, and  has  been  introduced  into  clinics  where  it  is  daily  rendering 
great  service.  It  might  be  asked,  therefore,  whether  the  measurements 
of  the  internal  surfaces  could  not  also  find  clinical  application.  Indeed 
there  often  exist  between  the  astigmatism  indicated  by  the  ophthal- 
mometer  and  subjective  astigmatism,  differences  the  cause  of  which 


72  PHYSIOLOGIC  OPTICS 

it  is  very  natural  to  look  for  in  the  internal  surfaces,  and  which  we 
might  hope  to  disclose  by  these  methods.  I  have  made  some  measure- 
ments of  this  character,  but  I  do  not  think  they  have  a  great  future. 
They  are  always  very  complicated;  it  would  be  necessary,  in  fact,  to 
measure  the  radius  of  each  surface  at  least  in  two  meridians,  and  as 
each  radius  calls  for  two  measurements  (of  the  surface  and  the  center) 
this  would  involve  already  12  measurements ;  it  would  then  be  necessary 
for  us  to  calculate  the  real  values  in  order  to  deduct  the  astigmatism 
of  each  surface  and  lastly  to  combine  these  astigmatisms  with  that  of  the 
anterior  surface  of  the  cornea.  This  is  already  sufficiently  complicated, 
but  it  becomes  more  so  if,  as  is  probable,  the  main  meridians  of  the 
internal  surfaces  coincide  neither  with  one  another  nor  with  those  of 
the  anterior  surface  of  the  cornea.  —  It  is  true  that  it  would  be  possible 
to  simplify  the  methods  for  practical  application,  and  to  replace  the 
calculations  by  approximations,  but  I  do  not  think  the  result  is  worth 
the  trouble,  more  especially  as  it  is  probable  that  we  frequently  woulfl 
not  find  what  we  look  for,  the  explanation  of  the  differences  between 
ophthalmometry  and  subjective  astigmatism,  for  these  differences  are 
probably  frequently  due  to  the  fact  that  the  peripheral  parts  of  the 
cornea  have  an  astigmatism  different  from  that  of  the  central  parts, 
which  we  measure  with  the  ophthalmometer. 

Bibliography.  —  Aubert  (H.).  Pfluger's  Archiv.  Bd.  35,  p.  597, 1885.  —  Javal  (E.). 
Memoires  tfophtalmometrie.  Paris,  1890.  —  Sulzer  (D.).  La  forme  de  la  cornee  humaine  et  son 
influence  sur  la -vision.  Arch,  d'opht.,  1891.  —  Eriksen.  Hornhindemaalinger  (Danish).  Ara- 
hus,  1893.  — Tscherning  (M.).  Beitrage  zur  Dioptrik  des  Auges  (Zeitschrift  fur  Psychologic 
und  Physiologie  der  Sinnesorgane,  III,  p.  429).  —  Brudzewski  (K.).  Beitrag  zur  Dioptrik  des 
Auges.  Arch,  fur  Augenheilkunde.  XL,  3. 


CHAPTER  V. 

CIRCLES  OF  DIFFUSION  ON  THE  RETINA. 

36.  Definition.  —  Receiving  on  a  screen  the  image  of  a  distant  lu- 
minous point,  and  moving  the  screen  forwards  and  backwards,  we  see 
that  there  is  only  one  position  in  which  there  is  formed  a  distinct  image 
of  the  point.  In  every  other  position  we  see  on  the  screen  a  luminous 
spot  of  the  same  form  as  the  aperture  of  the  lens,  which  spot  is  the  larger 
the  farther  it  is  removed  from  the  distinct  image.  This  luminous  spot 
is  called  circle  of  diffusion. 

The  same  thing  happens  in  the  eye,  with  this  difference  that,  not  being 
able  to  move  the  retina  backwards  or  forwards,  we  move  the  luminous 
point  which  amounts  to  the  same.  The  round  form  of  the  image  of 
diffusion  is  due  to  the  round  form  of  the  pupil  ;  if  we  look,  for  example, 
through  an  aperture  which  is  triangular  and  smaller  than  the  pupil,  the 
image  of  diffusion  is  triangular 
and  is  somewhat  improperly 
called  circle  of  diffusion. 

It  is  easy  to  calculate  the  size 
of  the  circle  of  diffusion  (fig. 
54).  If  the  diameter  of  the  pupil 
(of  exit)  be  designated  by  />,  its 

distance  from  the  retina  by  a  and  the  distance  of  the  distinct  image  from 
the  retina  by  d,  we  have  for  the  diameter  of  the  circle  of  diffusion  the 
expression 


If,  instead  of  a  luminous  point,  we  observe  an  object  the  image  of 
which  is  formed  in  front  of  or  behind  the  retina,  each  point  of  the  object 
produces  on  this  membrane  a  circle  of  diffusion  which  is  overlapped 
by  the  next  circle,  except  near  the  borders  of  the  diffuse  image.  There 
is  also  formed  around  the  shape  of  the  object  a  border,  the  width  of 

73 


74  PHYSIOLOGIC   OPTICS 

which  is  equal  to  half  of  the  diameter  of  a  circle  of  diffusion,  and  the 
intensity  of  which  diminishes  towards  the  periphery.  The  object  is, 
therefore,  seen  a  little  enlarged  and  with  ill-defined  borders. 

37.  Line  of  Sight.  —  When  we  perform  the  act  of  sighting  we  try  to 
-make  two  points,  situated  at  different  distances,  coincide ;  as  we  can  only 
see  one  point  distinctly  at  once,  it  is  generally  supposed  that  we  make 
the  image  of  one  of  the  points  coincide  with  the  center  of  the  circle  of 
diffusion  of  the  other.  Now  the  center  of  the  circle  of  diffusion  cor- 
responds with  the  middle  of  the  pupil ;  it  would  be  necessary,  therefore, 
to  place  the  second  point  on  the  line  which  joins  the  point  which  is 
fixed  to  the  center  of  the  apparent  pupil,  a  line  which  is  called  the  line 
of  sight.  This  reasoning  is  subject  to  caution.  Indeed,  in  order  to  be 
able  to  sight,  it  is  necessary  to  see  the  second  point  pretty  distinctly, 
which  requires  that  it  be  not  too  far  removed,  optically,  from  the  point 
fixed.  The  circle  of  diffusion  of  the  point  of  sight  is,  therefore,  so  small 
that  we  commit  only  a  very  small  error  when  we  consider  it  as  a  point. 
We  must  also  note  that  the  rule  according  to  which  the  circle  of  diffusion 
should  everywhere  have  the  form  of  the  pupil,  is  not  strictly  correct. 
By  reason  of  astigmatism  and  other  irregularities  of  the  eye,  there 
nearly  always  exists,  as  we  shall  see  in  chapter  X,  a  part  in  front  of  or 
behind  the  focus,  where  the  circle  of  diffusion  is  far  from  having  the 
form  of  the  pupil ;  it  assumes  more  or  less  irregular  forms,  and  the  light 
is  no  longer  distributed  in  a  regular  manner.  In  sighting,  then,  we 
make  the  image  of  the  point  fixed  coincide  with  the  brightest  part  of 
the  circle  of  diffusion,  which  has  nothing  to  do  with  the  center  of  the 
pupil.  In  order  not  to  complicate  the  terminology,  it  would,  therefore, 
be  preferable  to  dispense  with  the  expression  line  of  sight. 

38.  Accommodation.  —  We  know  that  the  eye  can  change  its  focus, 
adapting  itself  for  shorter  distances  than  that  for  which  it  is  adapted  in 
a  state  of  repose.  Holding  a  book  at  50  centimeters  and  placing  a  veil 
between  the  book  and  the  eyes,  at  20  centimeters,  we  can  see  distinctly, 
sometimes  the  threads  of  the  veil,  and  sometimes  the  letters.  —  If  we 
illuminate  the  fundus  of  an  emmetropic  eye  with  the  aid  of  a  plane 
mirror,  by  using  a  flame  placed  at  a  great  distance,  we  see  a  distinct 
image  of  the  flame  projected  on  the  fundus  of  the  eye,  if  the  observed 
person  looks  in  the  distance.  If,  on  the  contrary,  he  fixes  an  object 
located  nearer,  the  image  forms  a  circle  of  diffusion  which,  most  fre- 
quently, fills  the  entire  pupil.  The  contrary  takes  place  when  the  flame 
is  placed  at  a  short  distance. 


CIRCLES  OF  DIFFUSION  OF  THE  RETINA  75 

39.  Experiments  of  Czermak,  Scheiner  and  Mile.  —  Looking  towards 
.an  illuminated  surface  (the  sky,  for  example)  through  a  pin-hole  made 
in  a  dark  screen,  we  see  the  opening  under  the  form  of  a  circle  of 
diffusion.    If  we  move  a  second  screen,  held  nearer  the  eye,  in  front  of 
the  opening,  it  seems  to  move  in  a  direction  contrary  to  that  in  which 
it  really  does  move.    If,  on  the  other  hand,  we  move  the  second  screen 
in  front  of  the  first,  it  seems  to  move  in  the  direction  of  its  real  displace- 
ment (Czermak). 

Looking  towards  an  illuminated  surface  through  two  openings,  the 
distance  of  which  is  smaller  than  the  diameter  of  the  pupil,  we  see  two 
circles  of  diffusion  which  partly  overlap.  A  needle  is  then  placed  so 
that  we  see  it  in  the  part  common  to  the  circles  of  diffusion,  and  another 
farther  away  in  the  same  direction.  That  one  of  the  two  needles  which 
we  fix  is  seen  single,  the  other  double.  If  it  is  the  nearer  needle  that  is 
seen  double,  the  image  on  the  left  disappears,  if  we  cover  the  opening 
on  the  right,  (i)  If  it  is  the  other  needle  that  is  seen  double,  the  con- 
trary takes  place  (Scheiner).  —  It  is  easy  to  repeat  this  experiment  with 
a  lens,  and  it  is  also  a  very  good  way  of  determining  the  focal  distance 
of  the  latter  (by  replacing  the  needle  by  a  luminous  point). 

If  we  look  at  the  more  distant  of  the  two  needles  in  the  experiment 
of  Scheiner  through  a  single  small  opening,  we  shall  see  that  a  slight 
movement  of  the  screen  causes  the  nearest  needle  to  move  in  the  con- 
trary direction.  On  fixing  the  nearer  of  the  two  needles  the  other 
seems  to  move  in  the  same  direction  as  the  screen  (Mile). 

It  is  easy  to  account  for  these  phenomena  when  we  sketch  the  course 
of  the  rays,  not  forgetting  that  the  eye  inverts  the  phenomena  when 
projecting  them  outwards. 

40.  Optometer  of  Thomas  Young.  (2)  —  The  experiment  of  Scheiner 
forms  the  basis  of  the  optometer  of  Thomas  Young,  which  appears  to 

( 1)  To  reader  the  experiment  more  striking  to  my  pupils,  I  had  a  plate  of  red  gelatine  glued  in  front 
•of  the  opening  on  the  right.  But,  after  having  explained  the  theory  of  the  experiment,  I  met  with  very 
vigorous  protestations ;  all  declared  that  it  was  the  needle  on  the  right  which  appeared  red.  It  is  thus, 
in  fac",  when  we  look  towards  the  sky,  but  we  must  not  conclude  from  this  that  it  is  the  needle  on  the 
right  which  belongs  to  the  opening  on  the  right.  The  phenomenon  is  analogous  to  that  of  colored 
shadows,  of  which  I  will  speak  in  chapter  XVII.  If  one  places  oneself  in  such  a  way  that  the  needle  is 
eliminated,  it  is  the  image  on  the  left  which  appears  red.  One  of  my  pupils,  M.  Johnsson,  has  studied 
the  chromatic  phenomena  which  are  observable  under  the  same  circumstances,  by  looking  at  the  needle 
towards  the  sky,  but  without  the  interposition  of  the  colored  plate.  One  sees  them  specially  well  by 
dilating  the  pupil  and  using  the  slits  of  the  optometer  of  Young.  When  the  needle  is  situated  on  the 
near  side  of  the  point  which  is  fixed,  one  of  the  images  is  seen  green,  the  other  purple  ;  each  image  is 
bordered  with  red  on  the  side  which  looks  towards  the  other  image,  with  blue  on  the  opposite  side. 
These  phenomena,  which  depend  on  the  chromatic  aberration  of  the  eye,  are  not  yet  well  explained. 

(2"1  Not  being  able  to  procure  any  part  of  this  instrument,  I  had  it  constructed  again  by  M.  Werlein, 
modernizing  it  a  little. 


76 


PHYSIOLOGIC  OPTICS 


me  to  be  one  of  the  most  important  instruments  for  the  study  of  physi- 
ologic optics.  It  has  the  form  of  a  little  rule.  On  one  of  the  faces  is 
drawn  a  fine  white  line  on  a  black  ground.  We  look  along  this  line, 
through  a  lens  of  +  10  D.  In  front  of  the  lens  moves  a  small  horizontal 
rule,  in  which  are  different  groups  of  slits  (fig.  5$a).  Placing  the  two 
slits,  which  are  at  the  middle  of  the  horizontal  rule,  in  front  of  the  lens, 
they  act  like  the  openings  in  the  experiments  of  Schemer.  Each  point 


Fig.  55.  —  Kules  of  the  optometer  of  Young. 

of  the  line  appears  double,  except  that  which  is  seen  distinctly ;  an 
emmetrope,  not  using  his  accommodation,  must,  therefore,  see  two  lines 
which  intersect  at  the  punctum  remotum,  or  artificial  far  point,  at  10  cm. 
from  the  eye.  To  determine  the  refraction  of  any  person  we  make  him 
look  in  the  instrument,  and  put  a  small  cursor  at  the  place  where  he 
sees  the  lines  intersect.  A  dioptric  scale,  placed  along  the  line,  then 
permits  the  refraction  to  be  read  off  directly.  —  We  then  determine 
the  near  point  (punctum  proximum)  in  the  same  manner.  —  The  other 
groups  of  slits  permit  the  determination  of  the  refraction  of  the  different 
parts  of  the  pupillary  space.  We  can  also  use  the  little  vertical  rule  (fig. 
51^)  which  has  the  form  of  a  very  pointed  triangle ;  by  lowering  it  more 
or  less,  we  eliminate  a  smaller  or  greater  part  of  the  middle  of  the  pupil. 
The  instrument  does  not  lend  itself  very  well  to  the  examination  of 
patients,  for  it  is  quite  difficult  for  an  inexperienced  observer  to  use  it 
without  using  his  accommodation.  For  one  who  can  control  his  accom- 
modation, the  instrument  permits  the  measurement  simultaneously  of 


CIRCLES  OF  DIFFUSION  OF  THE  RETINA 


77 


the  refraction  and  the  amplitude  of  the  accommodation;  the  refraction 
can  be  determined  in  different  meridians  by  making  the  instrument 
rotate  around  its  longitudinal  axis.  It  was  thus  that  Young  discovered 
the  astigmatism  of  his  own  eye. 

The  observations  made  with  this  optometer  are,  moreover,  of  the 
greatest  importance  for  the  study  of  the  nature  of  accommodation  (see 
chapter  XII). 

41.  Effects  of  the  Stenopaic  Opening.  —  Looking  through  an  opening 
smaller  than  the  pupil,  we  diminish  the  circles  of  diffusion  so  that  objects 
which  we  first  see  dimly  become  more  distinct.  This  is  why  myopes 
see  better  at  a  distance  by  looking  through  a  small  opening.  We  can 
also  make  use  of  it  as  a  magnifying  glass ;  we  can,  indeed,  move  very 
close  to  the  eye  the  object  which  we  desire  to  examine,  and  in  this  way 
obtain  a  very  large  retinal  image.  The  more  the  diameter  of  the  opening 
is  diminished,  the  more  distinct  the  image  becomes,  but  it  loses  at  the 
same  time  in  brightness.  We  cannot  exceed  a  certain  minimum  limit 
without  blurring  by  diffraction  the  distinctness  of  the  image,  (i) 

As  the  stenopaic  opening  effaces,  so  to  speak,  the  effect  of  the  anom- 
alies of  refraction,  it  is  harmful  in  all  cases  in  which  we  desire  to  deter- 
mine refraction.  This  is  why  we  place  patients  with  their  backs  towards 
the  window  when  we  examine  their  vision.  We  must  also  avoid  the 
small  apertures  in  the  ophthalmoscopes  which  are  used  to  determine 
refraction;  a  too  strong  illumination  is  equally  hurtful. 


Fig.  56.  —  Magnification  by  means  of  the  stenopaic  opening. 

Examining  an  object  placed  very  near  the  eye  through  a  stenopaic 
opening,  we  shall  see  that  the  object  seems  to  enlarge  as  we  gradually 
move  the  screen  away 'from  the  eye.  Following  is  the  explanation  of 
this  fact. 


(1)  Looking  at  a  luminous  point  which  we  see  distinctly,  through  a  very  fine  opening,  we  observe 
that  it  becomes  enlarged  into  a  small  luminous  surface  surrounded  with  brilliant  rings.  This  effect  of 
diffraction  begins  to  make  itself  slightly  felt  starting  from  an  aperture  of  the  pupil  or  of  the  opening 
of  about  2  millimeters. 


78  PHYSIOLOGIC  OPTICS 

Let  AB  (fig.  56)  be  an  object,  and  A^  its  image  formed  by  the  optic 
system  of  the  eye.  As  the  object  is  near  the  eye,  the  image  is  formed 
quite  a  distance  behind  the  retina.  To  determine  the  position  of  the 
indistinct  image  on  the  retina,  we  draw  the  ray  Ac  passing  through  the 
middle  of  the  pupil  of  entrance;  after  refraction  it  continues  its  course 
as  if  it  came  from  clt  the  center  of  the  pupil  of  exit.  Its  direction  is 
AV-,,  since  it  must  pass  through  A',  the  image  of  A.  The  point  a  is, 
therefore,  the  middle  of  the  circle  of  diffusion  which  A  forms  on  the 
retina,  and  ab  is  the  diameter  of  the  image  of  diffusion.  —  Let  us  now 
interpose  the  screen  EE  with  its  stenopaic  opening.  The  only  ray  which 
passes  from  A  through  this  opening  takes  the  direction  AK  and,  after 
refraction,  the  direction  KXA' ;  it  meets  the  retina  at  at  and  a^  b1  is  the 
size  of  the  retinal  image.  We  see  that  this  image  is  larger  than  ab  and 
that  it  would  become  larger  still  if  we  moved  the  screen  farther  away.  — 
Myopes  looking  at  distant  objects  through  a  stenopaic  opening  see  them 
diminish  if  the  opening  be  moved  away  a  little. 

Bibliography.  —  The  study  of  the  influence  of  circles  of  diffusion  on  vision  has  been 
very  much  neglected  by  modern  authors.  The  best  work  done  on  this  question  is  the  fol- 
lowing, which  dates  from  the  last  century. 

Jurin  (J.).  Essai  sur  la  vision  distincte  el  indistinct*,  in  Robert  Smith,  Cours  complet  d'op- 
tiquc,  translated  by  Pezenas,  Paris,  1767.  —  Scheiner  (C.).  Oculus.  Innspruck,  1619. — 
Mile  (J.).  Pogg.  Ann.,  XLII,  40.  —  (Euvres  de  Young  edited  by  Tscherning,  page  112.  — 
Tscherning  (M.).  L'optomdre  de  Young  et  son  emploi.  Arch,  d e  physiol.  October,  1894. 


CHAPTER  VI. 
ANOMALIES  OF  REFRACTION. 


42.  General  Remarks.  —  We  have  thus  far  treated  the  optic  system  of 
the  eye  as  if  it  were  perfect,  but  it  has  really  many  defects.  Helmholts- 
said  that  if  an  optician  had  delivered  to  him  an  optic  instrument  as  im- 
perfectly made  as  the  eye,  he  would  have  considered  himself  within  his 
right  in  refusing  it ;  expressing  himself  in  quite  forceful  language.  The 
remark  of  M.  Mascart  appears  to  me  nearer  the  truth.  He  said  that  the 
eye  has  all  possible  defects,  but  only  to  such  an  extent  that  they  are  not 
harmful.  We  have  already  seen  that  this  is  the  case  with  diffraction, 
which  begins  to  make  itself  felt,  starting  from  a  pupillary  diameter  of 
2.  millimeters,  almost  the  lowest  limit  of  this  diameter.  It  is  the  same 
with  chromatic  aberration,  spherical  aberration,  etc.  An  optician  need 
not  be  so  careful  with  an  objective,  the  images  of  which  are  intended  to 
be  magnified  five  times,  as  with  another  the  images  of  which  are  to  be 
magnified  twenty  or  thirty  times.  In  the  same  way  eyes  frequently  have 
all  the  visual  activity  we  can  expect  considering  the  retinal  structure, 
and  a  greater  degree  of  optic  perfection  would  be  superfluous.  It  is 
true  that  many  eyes  which  are  considered  normal,  have  optic  defects 
which  diminish  their  visual  acuity,  which  should  be  nearly  double  that 
called  normal  acuity;  but  for  most  occupations,  the  acuity  known  as 
normal  amply  suffices. 

We  can  divide  anomalies  of  refraction  into  three  groups: 

i°.  ANOMALIES  "OF  THE  SCREEN." 

a.  Axial  myopia.  —  Screen  is  too  far  away  from  the  optic  system. 

b.  Axial  hypermetropia.  —  Screen  is  too  near  the  optic  system. 

c.  Oblique  position  of  the  screen.  —  This  last  anomaly  is  not  generally 
recognized.    It  seems  to  play  a  part  in  diminishing  the  visual  acuity  in 
certain   forms    of   very   high    myopia,   in    which    the    summit    of   the 
staphyloma  does  not  correspond  exactly  with  the  fovea.    It  is  evident 


80  PHYSIOLOGIC  OPTICS 

that,  if  the  optic  system  of  the  eye  were  perfect,  all  the  rays  emanating 
from  a  point  would  meet  exactly  in  a  point  on  the  screen,  and  the 
obliquity  of  the  latter  would  play  no  part,  for  the  extent  of  distinct 
vision  is  so  small  that  the  difference  of  distance  of  the  different  parts  of 
the  image  from  the  optic  system  cannot  have  much  influence.  But  if 
the  rays  do  not  meet  exactly  in  a  point,  as  is  nearly  always  the  case,  it 
is  clear  that  the  circle  of  diffusion  on  the  retina  must  be  larger  when 
the  retina  is  placed  obliquely,  and  that  this  must  diminish  visual  acuity. 

2°.  ANOMALIES  OF  THE  REFRACTING  SURFACES. 

Myopia  )     £ 

\  of  curvature. 
Hypermetropia  j 

Regular  astigmatism. 
Spherical  aberration. 
Chromatic  aberration. 
Keratoconus. 
Lenticonus. 
Aphakia. 

Luxation  of  the  crystalline  lens. 

All  the  forms  which  are  classified  under  the  name  of  irregular  astigma- 
tism. 

3°.  ANOMALIES  OF  THE  INDICES. 

False  lenticonus. 

The  anomaly  which  Demicheri  has  recently  described  under  the  name 
of  false  lenticonus  is  the  only  anomaly  of  the  indices  which  has  been 
established  up  to  the  present.  In  these  cases  we  see  with  the  ophthalmo- 
scope the  same  play  of  shadows  that  is  characteristic  in  keratoconus ;  it 
is  due  to  a  great  difference  of  refraction  between  the  middle  of  the  pupil 
which  is  very  myopic  (as  high  as  10  D.  and  more),  and  the  periphery 
which  is  hypermetropic  (3  to  4  D).  The  explanation  is  probably  to  be 
found  in  a  diminution  of  the  index  of  the  peripheral  layers  of  the  crys- 
talline lens,  a  change  which  must  diminish  the  refraction  of  the  peri- 
pheral parts  of  the  pupil  and  greatly  increase  the  central  refraction, 
following  the  explanation  which  we  have  given  on  page  30.  We  find 
in  these  cases  the  images  of  Purkinje  doubled  (see  page  29),  the  surfaces 
of  the  nucleus  giving  rise  to  a  quite  regular  reflection;  these  cases  are 
analogous  to  that  which  I  have  found  in  the  case  of  the  eye  of  a  dead  ox, 
probably  also  due  to  the  imbibition  of  water  by  the  superficial  parts. 

43.  General  Eemarks  on  Ametropia.  —  We  designate  as  the  far  point 
(punctum  remotum)  the  place  for  which  the  eye  is  focused  when  in  a  state 


ANOMALIES   OF  REFRACTION  81 

of  repose.  It  is,  therefore,  the  conjugate  focus  of  the  fovea.  By  mak- 
ing an  effort  of  accommodation,  the  eye  can  focus  itself  for  shorter  dis- 
tances. The  nearest  point  for  which  the  eye  can  adapt  itself  is  called 
the  near  point  (punctum  proximum).  We  generally  express  the  distance 
of  the  near  point  and  that  of  the  far  point  in  dioptrics ;  the  difference 
between  the  two  numbers  is  called  the  amplitude  of  the  accommodation. 
The  determination  of  the  far  -point  is  quite  easy,  and  forms  an  important 
part  of  the  work  of  the  oculist ;  that  of  the  near  point  is  not  very  certain, 
since  its  position  depends  on  an  effort  of  the  patient,  the  strength  of 
which  may  vary  from  day  to  day ;  for  that  reason  the  determination  of 
the  near  point  is  frequently  neglected  in  clinics. 

We  consider  as  normal  the  emmetropic  eye,  that  is  to  say,  an  eye  such 
that,  in  a  state  of  repose,  the  image  of  distant  objects  is  formed  on  the 
retina.  In  the  myopic  eye  this  image  is  formed  in  front  of,  in  the  hyper- 
metropic eye  behind,  the  retina.  We  designate  these  two  anomalies  under 
the  common  name  of  ametropia.  The  emmetropic  eye  has  its  far  point 
situated  at  infinity,  that  of  the  myopic  eye  is  at  a  finite  distance.  As  to 
the  hypermetropic  eye,  its  remote  point  is  virtual.  It  is  necessary  that 
the  rays  converge  before  entering  the  eye  in  order  that  they  may  re- 
unite in  a  point  on  the  retina.  This  point  towards  which  the  rays  must 
converge,  before  entering  the  eye,  and  which  is  consequently  situated 
behind  the  latter,  is  the  far  point;  its  distance  is  to  be  put  down  as  nega- 
tive. The  degree  of  ametropia  is  indicated  by  expressing  in  dioptrics 
the  distance  of  the  eye  from  the  remote  point,  (i) 

In  the  great  majority  of  cases,  myopia  and  hypermetropia  are  due  to 
an  anomaly  in  the  length  of  the  eye:  the  myopic  eye  is  too  long,  the 
hypermetropic  eye  too  short.  An  increase  or  a  diminution  of  I  milli- 
meter in  the  axis  of  the  eye  corresponds  to  an  ametropia  of  two  dioptrics 
and  a  half.  Let  us  place  in  the  formula  of  Newton,  /x  /2  =  Ft  F2,  the 
values  of  the  simplified  eye  Fx  =  17  millimeters,  F2  =  22.7,  and  we  will 
have  /!  /2  =  386,  in  which  formula  /x  is  the  distance  of  the  far  point  from 
the  anterior  focus  and  /2  the  distance  of  the  retina  from  the  posterior 
focus  of  the  eye.  If  L  =  1  millimeter,  /x  =  386  millimeters,  which  cor- 
responds to  about  2.5  D. ;  if  /2  =  2  millimeters,  /t  =  193  millimeters  or 
about  5  D.,  and  so  on. 

Myopia  is  corrected  by  placing  in  front  of  the  eye  a  concave  glass  so 
that  the  image  which  it  forms  of  distant  objects  may  be  situated  at  the 

(1)  From  which  part  of  the  eye  one  should  start  to  calculate  ametropia  is  a  disputed  question;  it 
seems  to  me  that  the  simplest  way  is  to  calculate  it,  starting  from  the  summit  of  the  cornea.  Some 
have  preferred  to  calculate  it  from  one  or  other  of  the  cardinal  points  of  the  optic  system,  but  as  these 
points  have  not  the  same  position  in  all  eyes,  nor  in  all  the  meridians  of  the  same  eye,  nor  even  for 
all  parts  of  the  same  meridian,  confusion  would  result. 


82 


PHYSIOLOGIC  OPTICS 


far  point  of  the  eye.  On  account  of  the  distance  of  the  glass  from  the 
eye  its  focal  distance  is  a  little  shorter  than  the  distance  of  the  eye  from 
its  far  point.  The  subjective  examination  always  results,  therefore,  in 
our  finding  a  somewhat  higher  myopia  than  really  exists.  The  difference 
is  insignificant  for  low  degrees  of  myopia,  considerable  for  high  de- 
grees. If  we  move  the  glass  away  from  the  eye,  its  effect  diminishes.  — 
When  selecting  the  correcting  glass,  we  must  take  great  care  to  select 
the  weakest  concave  glass  which  corrects,  because  young  myopes  see 
as  well  with  stronger  glasses,  the  excess  of  correction  being  neutralized 
by  accommodation.  After  having  found  the  correcting  glass,  we  may 
try  the  effect  of  moving  it  gradually  away  from  the  eye.  If  the  patient 
continues  to  see  well  the  glass  is  too  strong. 

Hypermetropia  is  corrected  by  means  of  a  convex  glass,  which  brings 
the  image  of  the  distant  object  to  the  far  point  situated  behind  the  eye. 
The  focal  distance  of  the  glass  being  a  little  greater  than  the  distance 
of  the  eye  from  the  far  point,  the  correcting  glass  is  a  little  weaker  than 
the  hypermetropia.  The  hypermetrope  can  increase  the  strength  of  his 
glasses  by  moving  them  a  little  away  from  the  eye.  —  The  correcting 
glass  is  the  strongest  convex  glass  which  the  patient  tolerates  without 
loss  of  visual  acuity,  but  he  can  also  see  as  well  with  weaker  glasses  by 
using  his  accommodation. 


The  retinal  image  of  an  object  seen  under  a  given  angle  is  larger  in 
the  myopic  eye  and  smaller  in  the  hypermetropic  eye  than  in  an  emme- 
tropic  eye,  because  the  distance  of  the  posterior  nodal  point  from  the 
retina  is  greater  in  the  myopic  eye,  less  in  the  hypermetropic  eye.  — 
But,  this  effect  disappears  when  we  correct  the  ametropic  eye,  by  plac- 
ing the  correcting  glass  so  that  its  optic  center  coincides  with  the  an- 
terior focus  of  the  eye.  Then  the  image  is  always  the  same  size,  what- 
ever the  ametropia  may  be.  For,  the  rays  AO  and  BO  (fig.  57)  pass 
through  the  lens  without  deviation  and  are  parallel,  after  refraction  by 


ANOMALIES   OF  REFRACTION  83 

the  optic  system  of  the  eye,  so  that  the  size  of  the  image  is  always  the 
same,  whatever  may  be  the  distance  of  the  retina.  —  If  we  place  the  cor- 
recting glass  in  front  of  the  anterior  focus,  the  retinal  image  of  the 
myopic  eye  is  smaller,  that  of  the  hypermetropic  eye  larger,  than  the 
image  of  the  emmetropic  eye,  which  is  easy  to  see  by  a  construction 
analogous  to  that  of  fig.  57.  We  first  construct  the  image  formed  by 
the  glass,  and  draw  the  rays  passing  through  the  extremities  of  this 
image  and  through  the  anterior  focus. 

Patients  often  say  that  the  concave  glasses  diminish  objects.  This 
may  be  attributed  to  the  fact  that  the  glass  is  placed  in  front  of  the 
anterior  focus,  or  simply  to  the  fact  that  exterior  objects,  seen  distinctly, 
appear  smaller,  because  of  the  disappearance  of  the  circles  of  diffusion. 
But  the  cause  may  also  be  that  the  glass  is  too  strong;  for  if  the  patient 
uses  his  accommodation  the  anterior  focus  approaches  the  eye  and  the 
image  becomes  smaller  for  this  reason. 

44.  Optometers.  —  The  use  of  the  test  case  lenses  and  of  the  visual 
acuity  chart,  placed  at  a  distance,  is  always  the  best  of  the  subjective 
methods.  A  very  great  number  of  optometers  have  been  constructed, 
but  none  of  them  has  succeeded  in  superseding  the  test  case ;  they  have 
this  defect  in  common  that  they  superinduce  an  effort  of  accommoda- 
tion which  makes  the  myopia  appear  too  strong.  The  best  are  those 
which  are  operated  at  a  great  distance,  like  the  optometer  of  Javal,  but 
even  these  seem  sometimes  to  give  too  strong  degrees  of  myopia. 
The  optometer  of  Javal  is  composed  of  two  discs,  nearly  like  the  discs 
of  the  ophthalmoscope  for  refraction,  but  much  larger :  one  of  the  discs 
has  spherical  lenses,  the  other  cylindrical  lenses;  a  special  mechanism 
permits  the  axis  of  all  the  cylindrical  lenses  to  be  adjusted  in  the  direc- 
tion we  desire.  —  Other  optometers  are  founded  on  the  use  of  a  single 
convex  lens;  by  displacing  the  object  in  relation  to  this  lens,  we  can 
form  the  image  of  it  at  any  distance  whatever,  and  thus  find  the  place 
where  it  appears  distinct.  Optometers  of  this  kind  have  been  con- 
structed by  Coccms,  Bonders,  Sous,  and  many  others.  The  optometer  of 
Grade  was  a  Galilean  telescope;  we  know  that  myopes  are  obliged  to 
shorten  their  opera  glasses  to  see  distinctly.  By  providing  the  opera 
glass  with  a  scale  it  may,  therefore,  be  used  as  an  optometer.  —  So 
also  may  the  telescope,  the  use  of  which  was  proposed  by  Hirschbcrg. 

Among  all  these  optometers  I  shall  mention  specially  only  that  of 
Badal,  on  account  of  its  admirable  principle.  It  is  composed  of  a  single 
convex  lens,  the  focus  of  which  coincides  with  the  anterior  nodal  point 
of  the  eye.  The  position  of  the  latter  is  made  secure  by  an  eye-rest.  A 


84 


PHYSIOLOGIC  OPTICS 


diminished  copy  of  the  chart  of  Snellen  is  placed  on  the  other  side  of  the 
lens,  movable  forwards  and  backwards.  By  displacing  the  object  we 
can  make  the  image  appear  anywhere,  and  it  is  easy  to  see  (fig.  58)  that 
the  retinal  image  remains  always  the  same  size,  no  matter  whether  the 


Fig.  58.  —  Principle  of  Badcti. 

object  is  at.  bb  or  at  aa,  etc.  We  can  therefore  measure  the  visual 
acuity  with  this  optometer.  The  same  result  is  obtained  by  making  the 
focus  of  the  lens  coincide  with  the  anterior  focus  of  the  eye  (fig.  59). 


Fig.  59. 


45.  Myopia.  —  There  exist  two  forms  of  axial  myopia,  one  which  de- 
pends on  near  work,  and  one  which  does  not.  (i) — Myopia  from  near  work 
appears  usually  at  an  age  ranging  from  6  to  15  years;  it  often  stops  at 
the  age  of  25  years.  It  attains  medium  degrees  and  does  not  seem  to 
exceed  the  limit  of  9  D.  Complications,  except  staphyloma,  are  rare. 

Dangerous  myopia  is  sometimes  congenial  and  stationary ;  as  a  rule  it 
develops  in  early  infancy,  and  continues  to  increase  during  the  whole 
life.  At  the  age  of  20  years  it  generally  exceeds  9  D.  This  form  of 
myopia  is  to  be  considered  as  a  malignant  choroiditis,  and  it  is  to  it  that 
dangerous  complications  of  myopia  belong;  like  most  choroidal  affec- 
tions it  seems  to  be  a  little  more  prevalent  among  women. 

In  1882  and  1883  I  examined  about  7,000  young  Danish  conscripts, 
by  determining  their  refraction  by  means  of  the  upright  image.  The 
influence  of  near  work  is  seen  in  the  following  list: 

(1)  Even  eliminating  these  two  forms  of  myopia,  it  is  probable  that  there  would  still  remain  a  cer- 
tain number,  due  to  a  congenital  disagreement  between  the  optic  system  and  the  length  of  the  axis  of 
the  eye,  for  it  is  not  probable  that  all  normal  eyes  are  constructed  so  as  to  be  exactly  emmetropic.  — 
But  myopia  between  2  D.  and  9  D.  is  so  rare  among  uneducated  persons,  that  this  third  form  must  com- 
prise only  light  degrees. 


ANOMALIES   OF  REFRACTION 


85 


Myopes. 

Students 32  per  cent. 

Persons  employed  in  offices  and  in  trade 16       — 

Artists,  etc 13       — 

Tailors,  shoemakers,  etc 12       — 

-,,-  f  Workmen  (hard  labor) 5  per  cent. 

\  Agriculturists  (peasants) 2       — 


The  distribution  of  the  two  forms  of  myopia  in  the  two  groups  was 
the  following: 


I 

II 


In  all. 
2,336 
5,187 


Myopes  <  9  D. 
407  (17  per  cent.) 
169  (  3       —      ) 


Myopes  >  9  D. 
13  (0.56  per  cent.) 
38  (0.73       —      ) 


90  *f 


80  SS 


60  §* 


sow 


20  S| 


•oil 


Hyper-  a       e      v      z 

netronia  9        7         S        5 


metropia 


D  Myopia 


Fig.  60.  —  Distribution  of  the  anomalies  of  refraction  among  the  young  population  of 

Copenhagen. 
Educated.  Uneducated. 


We  see  that  the  very  great  frequency  of  myopia  in  the  educated  classes 


86  PHYSIOLOGIC   OPTICS 

comprises  only  the  lowest  degrees.  The  very  high  degrees  are  rather 
more  frequent  in  the  illiterate  (fig.  60).  —  Among  the  peasants  I  have 
even  met  more  cases  of  myopia  greater  than  9  D.  than  of  myopia 
between  2  D.  and  9  D. 

It  is,  therefore,  a  great  exaggeration  to  regard  myopia  from  near 
work  as  a  public  calamity,  as  is  done  especially  in  Germany.  One  exag- 
geration leads  to  another.  It  was  thought  formerly  that  myopic  eyes 
were  stronger  than  others  because  they  did  not  become  presbyopic. 
After  the  discovery  of  the  ophthalmoscope  very  grave  complications  in 
cases  of  strong  myopia  were  continually  met  with,  and  thus  originated 
the  idea  expressed  in  the  celebrated  phrase  of  Bonders,  "I  do  not  hesi- 
tate to  declare  that  every  myopic  eye  is  a  diseased  eye,"  a  phrase  which 
Cohn  adopted  as  his  motto  in  the  first  of  the  great  compilations  of 
statistics  of  school  children  ever  made.  Later,  many  others  were  made, 
but  without  important  results.  They  show  conclusively  that  myopia 
is  more  frequent  and  more  pronounced  in  the  higher  classes  of  the 
schools ;  but  as  the  pupils  of  these  classes  are  older,  and  as  the  myopia 
is  a  condition  that  develops  with  age,  these  statistics  do  not  establish 
definitely  the  influence  of  near  work. 

A  satisfactory  explanation  of  the  mechanism  by  which  near  work 
produces  myopia  has  not  yet  been  given.  Danders  named  three  factors : 
first,  the  inclined  position  of  the  head  which  produces  hyperemia  of  the 
globe  with  a  tendency  to  distention;  second,  the  fatigue  of  the  eyes, 
which  would  be  the  result  of  prolonged  reading,  and  which  would  also 
produce  hyperemia;  third,  the  compression  which  the  external  muscles 
would  exercise  on  the  eye,  during  convergence  for  a  near  point.  —  Arlt, 
who,  by  his  autopsies,  proved  for  the  first  time  in  1854  that  myopia  is 
due  to  a  lengthening  of  the  globe,  laid  special  stress  on  the  action  of  the 
superior  oblique  while  reading.  The  eye  being  directed  downwards, 
this  muscle  may,  indeed,  compress  one  of  the  veins  and  thus  produce 
the  development  of  hyperemia.  Stilling  tried  to  further  develop  this 
theory  by  finding  the  predisposition  to  myopia  in  a  special  form  of  the 
orbit  (very  low  —  Hypoconchid)  which  would  give  to  the  muscle  a  direc- 
tion more  likely  to  compress  the  eye. 

In  spite  of  the  slight  degree  of  accommodation  which  myopes  need  (i), 

(1)  It  is  possible  that  myopes  often  accommodate  more  than  we  think.  la  low  degrees  they  fre- 
quently work  within  their  far  point,  because  by  bringing  the  work  near  they  can  see  more  detail.  As 
to  high  degrees,  other  circumstances  may  bring  about  a  quite  remarkable  accommodation.  This  is  why 
Jzval  said  that  a  myopic  eye  may  be  focused  at  once  for  the  extremities  and  the  middle  of  a  line  of  a 
book.  If  the  myopia  is  10  D.,  the  length  of  the  line  is  10  cm.,  and  if  the  ends  of  the  line  are  seen  dis- 
tinctly without  accommodation,  the  patient  is  obliged  to  accommodate  about  two  dioptries  when  read- 
iag  the  middle,  unless  he  keeps  the  book  or  his  head  in  continuous  motion,  or  contents  himself  \vith 
seeing  diffusely  a  part  of  the  line. 


ANOMALIES   OF  REFRACTION  87 

the  theory  of  the  accommodative  origin  of  myopia  has,  however,  many 
believers,  and  I  think  they  are  right;  but  as  the  mechanism  of  accom- 
modation was  scarcely  known  until  recent  times,  it  is  not  wonderful 
that  the  solution  of  the  problem  of  myopia  from  near  work  was  sought 
in  vain. 


46.  Selection  of  Spectacles.  —  Although  myopia  from  near  work  is  not 
to  be  considered  as  a  true  diseased  condition  of  the  eye,  it  always  causes 
a  disagreeable  feeling  which  it  is  our  duty  to  prevent  as  much  as  possible. 
As  it  is  near  work  which  produces  myopia,  young  myopes  must  be  made 
to  work  at  as  great  a  distance  as  possible;  and,  on  account  of  the 
probable  influence  of  accommodation,  we  must  suppress  the  latter  as 
much  as  possible,  or  annul  it.  —  We  are  very  frequently  consulted  on  the 
question  of  glasses  by  parents  who  are  worried  at  seeing  their  children 
become  myopes.  —  If  the  myopia  is  low,  under  three  dioptrics,  we  give 
correcting  glasses  for  distant  vision,  and  nothing  for  near  vision,  (i)  rec- 
ommending the  patient  to  be  careful  as  to  the  distance  of  the  book  while 
reading.  We  place  the  normal  distance  for  work  at  33  centimeters.  —  If 
the  myopia  exceeds  three  dioptrics  we  give  for  near  vision  correcting 
glasses  diminished  by  3  D.  For  example,  if  the  myopia  is  6  D.  we  give 
3  D.  for  near  vision.  For  distant  vision  we  may  give  correcting  glasses 
or  a  supplementary  glass  to  superimpose  on  the  spectacles.  —  But,  in 
giving  concave  glasses  for  near  vision  we  must  forcibly  impress  upon 
myopes  the  necessity  of  observing  the  minimum  distance  of  33  centi- 
meters when  working;  otherwise  the  glasses  would  be  rather  harmful 
by  superinducing  an  effort  of  accommodation  which  might  cause  the 
myopia  to  increase. 

When  the  myopia  exceeds  9  D.,  it  becomes  necessary  to  regard  it  as 
dangerous,  and  great  care  in  the  use  of  the  eyes  must  be  recommended. 
Generally  it  is  preferable  not  to  completely  correct  myopia,  but  only 
sufficiently  so  that  the  patient  may  not  be  too  much  annoyed  in  moving 
around.  As  the  acuity  is  frequently  diminished  we  can  no  longer  insist 
on  as  great  a  distance  for  near  work;  thus  we  may  give  correcting 
glasses  diminished  by  4  to  5  D.  for  near  work,  which  places  the  far  point 
at  25  or  20  centimeters  respectively.  —  The  patient  must  be  advised 
never  to  work  with  his  head  lowered;  in  the  latter  case  where  the  dis- 


(1)  [In  the  United  States  we  prefer  to  let  these  myopic  patients  wear  their  glasses  constantly,  especially 
as  these  eyes  are  usually  more  or  less  astigmatic.  The  success  of  this  method  is  proved  by  the  careful  in- 
vestigations of  Dr.  S.  D.  Risley.  See  his  article  on  School  Hygiene  in  the  System  of  Diseases  of  the  Eye 
iby  Norris  and  Oliver,  Philadelphia,  1897.]  — If. 


88  PHYSIOLOGIC  OPTICS 

tance  of  the  work  is  20  cm.  a  desk  must  be  used.  —  Patients  frequently 
ask  us  for  advice  as  to  illumination.  No  artificial  light,  except  an  arc 
lamp,  is  hurtful  to  the  eyes;  the  stronger  it  is  the  better,  because  arti- 
ficial illumination  never  attains  the  degree  of  illumination  of  a  bright 
day;  but  it  may  be  useful  to  protect  the  eyes  with  a  shade. 

When  the  myopia  is  very  high,  spectacles  are  frequently  of  no  service, 
as  the  patients  do  not  accept  them.  It  is  then  necessary  to  restrict  near 
work  as  much  as  possible.  For  distant  vision  a  small  telescope  some- 
times gives  good  service.  In  order  to  obviate  the  necessity  of  accom- 
modation, patients  should  be  advised  to  lengthen  it  as  much  as  possible. 

47.  Treatment  of  Myopia.  —  Each  of  the  two  theories  by  which 
myopia  from  near  work  has  been  explained  has  given  rise  to  a  treat- 
ment of  this  defect.  The  theory  of  convergence  led  to  the  attempt  to  stay 
the  progress  of  myopia  by  performing  a  tenotomy  of  the  external  rectus 
as  soon  as  there  was  a  slightly  pronounced  latent  divergent  strabismus 
(which  was  called  insufficiency  of  the  internal  recti  —  exophoria).  Certain 
surgeons  performed  thousands  of  operations  of  this  character:  the  result 
was  very  doubtful,  and  we  may  consider  this  operation  as  abandoned. 
The  theory  of  accommodation  led  to  treatment  by  atropine ;  but,  before 
speaking  on  this  subject,  I  shall  say  a  few  words  on  the  use  of  atropine 
for  the  determination  of  refraction,  a  method  which  is  still  very  much 
in  vogue  in  some  countries. 

De  Wecker  held  decided  views  on  the  abuse  of  atropine  in  ophthalmic 
practice,  and,  as  far  as  its  use  for  the  determination  of  refraction  is  con- 
cerned, I  am  in  perfect  agreement  with  him.  —  We  know  that  young 
hypermetropes  are  accustomed  to  correct  part  of  their  hypermetropia 
by  using  their  accommodation,  and  that  they  cannot  relax  this  accom- 
modation without  becoming  trained  to  it  by  means  of  convex  glasses> 
at  least  as  long  as  they  fix  a  specified  object.  To  make  all  the  hyper- 
metropia manifest  we  must  instil  atropine  in  order  to  paralyze  the  ac- 
commodation. It  is  this  perfectly  correct  observation  which  gave  rise 
to  the  idea  that  generally  a  better  determination  of  refraction  would  be 
obtained  by  using  atropine,  and  which  resulted  in  the  ciliary  muscle 
being  held  responsible  every  time  a  difference  of  refraction  before  and 
after  the  instillation  of  atropine  was  found.  By  putting  atropine  in  the 
emmetropic  eye  we  often  find  a  light  degree  of  hypermetropia,  which 
Bonders  was  wont  to  explain  by  assuming  a  "tonus  of  the  ciliary  muscle." 
Frequently  also  we  see  myopia  diminish  slightly  under  the  influence  of 
atropine,  and  this  diminution  ,has  been  attributed  to  the  existence  of  a 


ANOMALIES   OF  REFRACTION  ,  89 

"spasm  of  accommodation,"  which  would  disappear  as  soon  as  the  ac- 
commodative muscle  would  be  paralyzed. 

These  errors  originated  in  the  belief  that  refraction  must  necessarily 
be  the  same  in  the  whole  pupillary  space.  It  is  nothing  of  the  kind: 
there  nearly  always  exist  differences  which  are  frequently  very  consider- 
able. Thus  there  is  in  my  eye  a  relatively  great  difference,  nearly  4  D., 
between  the  upper  border  and  the  lower  border  of  the  pupil  (see  page 
145).  —  When  we  instil  atropine,  the  pupil  is  dilated  and  the  basilar  posi- 
tion of  the  cornea,  which  is  much  flattened,  comes  into  play.  As  the 
flattening  of  these  parts  is  often  considerable  enough  to  over-correct 
the  spherical  aberration,  we  find  that  the  refraction  of  these  peripheral 
parts  is  generally  less  than  that  of  the  central  parts.  A  quite  slight 
dilatation  of  the  pupil  suffices  in  order  that  the  area  of  these  parts,  which, 
in  ordinary  conditions,  are  excluded,  may  be  greater  than  that  of  the 
ordinary  pupil ;  it  is  this  fact  which  makes  us  judge  specially  by  them 
in  the  determination  of  refraction.  If  the  peripheral  flattening  of  the 
cornea  is  less,  or  if  the  extent  of  the  optic  part  exceeds  the  ordinary 
limits,  which  sometimes  happens,  we  may,  thanks  to  the  spherical  aber- 
ration, obtain  an  increase  of  refraction  by  instilling  atropine.  Such 
cases  have  been  observed,  among  others  by  Javal;  they  were  very  diffi- 
cult to  explain  with  the  ideas  which  have  been  held  on  the  subject  up- 
to  the  present,  since  it  could  not  be  supposed  that  the  use  of  atropine 
could  cause  a  spasm  of  the  accommodation.  We  observe  like  phenomena 
with  photographic  objectives  the  aberration  of  which  is  not  well  cor- 
rected ;  the  focus  changes  on  changing  the  aperture  of  the  diaphragm.  — 
Except  in  cases  of  latent  hypermetropia,  we  obtain,  therefore,  generally 
a  better  idea  of  ocular  refraction  by  the  ordinary  examination  without 
atropine. 

Atropine  treatment  has  been  used  in  cases  of  progressive  myopia;  the 
ciliary  muscle  would  be  kept  paralyzed  for  15  days  or  a  month,  in  order 
to  arrest  the  progress  of  the  myopia,  the  special  purpose  being  to  coun- 
teract the  spasm  of  accommodation,  which  was  supposed  to  be  the  cause 
of  the  progress  of  the  myopia.  This  treatment  does  not  seem  to  have 
been  effective.  —  In  cases  where  the  eyes  are  exposed  to  great  danger, 
for  example  in  detachment  of  the  retina,  it  may,  however,  be  useful  to 
procure  for  them  complete  rest  by  instilling  atropine  and  forbidding 
work  altogether  for  some  time. 

Some  years  ago,  on  the  advice  of  Fukala,  the  profession  began  to  treat 
high  degrees  of  myopia  by  removing  the  crystalline  lens,  generally  by  a 
discission  followed  by  extraction.  This  treatment,  which  Danders  pro- 


4)0  PHYSIOLOGIC   OPTICS 

nounced  criminal  at  a  time  when  surgical  operations  were  more  dan- 
gerous than  now,  often  seems  to  give  very  good  results,  not  only 
because  those  operated  on  become  emmetropic  or  nearly  so  after  the 
operation,  but  also  because  they  gain  considerably  in  visual  acuity  for 
distance.  We  have  already  seen  that  the  size  of  the  retinal  image  of  the 
myopic  eye,  corrected  by  a  glass  placed  at  the  anterior  focus,  is  equal  to 
the  image  of  the  emmetropic  eye.  Now,  in  the  emmetropic  eye  the  retina 
is  situated  about  16  millimeters  behind  the  posterior  nodal  point;  in 
a  myopic  eye,  which  has  become  emmetropic  by  the  extraction  of  the 
crystalline  lens,  the  retina  is  situated  at  the  posterior  focus  of  the  cornea 
•or  about  24  millimeters  from  the  nodal  point.  As  the  size  of  the  image 
depends  only  on  this  distance,  we  see  that  the  linear  enlargement  of  the 
image  by  the  operation  is  about  a  half.  Often  it  gains  still  more  because 
the  correcting  glass  is  placed  not  at  the  anterior  focus  but  a  little  in 
front,  which  has  the  effect  of  diminishing  the  image.  The  loss  of  accom- 
modation, which  is,  indeed,  of  very  little  use  to  myopes  of  a  high  degree, 
cannot  counterbalance  these  advantages ;  nevertheless  there  is  reason 
for  prudence  in  recommending  this  operation,  for  it  is  not  without 
•danger.  When  making  the  discission  (followed  by  paracentesis)  we 
may  fear  glaucomatous  complications  or  iridocyclitis  as  a  consequence 
of  a  too  great  swelling  of  the  crystalline  lens.  If  extraction  is  performed 
an  accidental  loss  of  the  vitreous  body  may  sooner  or  later  produce  a 
detachment  of  the  retina. 


48.  Hypermetropia.  —  The  hypermetropic  eye  is  too  short.  The  retina 
being  too  near  the  optic  system,  the  hypermetrope  cannot,  without  an 
effort  of  accommodation,  reunite  on  the  retina  parallel  or  diverging 
rays.  When  the  hypermetropia  is  high,  the  amplitude  of  accommoda- 
tion diminishing  with  age,  there  comes  a  time  when  the  patient  can  no 
longer  correct  his  hypermetropia  by  accommodation  (absolute  hyper- 
metropia). —  The  degree  of  hypermetropia  is  expressed  by  the  strongest 
convex  glasses  with  which  the  patient  can  distinguish  distant  objects 
distinctly.  To  disclose  all  the  hypermetropia,  it  is  often  necessary  to 
paralyze  the  ciliary  muscle  by  means  of  atropine,  because  the  patient 
has  formed  the  habit  of  accommodating  as  soon  as  he  fixes  an  object, 
and  he  cannot  suddenly  rid  himself  of  this  habit  even  when  we  put  before 
his  eye  a  convex  glass  which  should  eliminate  any  necessity  of  accom- 
modation. —  That  part  of  hypermetropia  which  we  cannot  make  man- 
ifest by  the  ordinary  examination  is  called  latent  hypermetropia  (Bonders)  ; 
it  diminishes  with  age,  and  it  need  not  be  regarded  as  a  very  definite 


ANOMALIES   OF  REFRACTION  91 

quantity.  We  can  often,  by  working  a  little  with  the  patient,  make  him 
accept  stronger  and  stronger  glasses.  In  the  dark  room  where  the 
patient  does  not  fix,  hypermetropia  frequently  becomes  manifest  in  its 
entirety  which  permits  it  to  be  determined  with  the  refraction  ophthal- 
moscope or  by  skiascopy. 

ACCOMMODATIVE  ASTHENOPIA.  —  The  hypermetrope,  being  obliged 
10  use  part  of  his  accommodation  to  neutralize  his  defect  of  refraction, 
generally  becomes  fatigued  more  quickly  than  the  emmetrope  by  near 
work.  The  essential  symptom  of  this  accommodative  asthenopia  is  that, 
while  reading,  the  letters  become  blurred.  When  this  symptom  appears, 
the  patient  reads  with  ease  for  some  time ;  then  the  letters  begin  to  be- 
come indistinct,  so  that  he  is  forced  to  rest  a  while.  If  he  begins  again 
he  gets  along  well  for  a  shorter  time  than  before,  after  which  the  same 
phenomenon  is  reproduced.  If  the  patient  still  continues  there  super- 
vene fatigue,  orbital  pains,  etc.;  but  these  phenomena  are  secondary, 
and  we  must  not,  from  their  appearance,  decide  on  hypermetropia  as 
the  cause  in  the  absence  of  the  essential  symptom,  viz.,  the  indistinctness 
of  the  letters  after  reading  for  some  time.  We  need  no  longer  attribute 
the  complaints  of  patients  to  a  low  degree  of  hypermetropia.  Low 
degrees  of  hypermetropia  manifest  themselves,  as  a  rule,  only  by  the 
premature  appearance  of  presbyopia.  We  may  easily  correct  a  low 
degree  of  hypermetropia,  even  in  young  people,  but  we  must  not  expect 
to  obtain  great  results.  The  complaints  of  the  patients  have  generally 
other  causes. 

Boehm,  Stellwag  and  others  recommended  the  use  of  convex  glasses 
in  cases  of  accommodative  asthenopia,  but  to  Danders  belongs  the  credit 
of  having  brought  them  into  general  use.  His  labors,  indeed,  con- 
tributed greatly  to  dispel  the  fear  which  earlier  oculists  had  of  strong 
convex  glasses.  They  considered  asthenopia  as  the  forerunner  of 
amblyopia,  and  believed  that  the  giving  of  convex  glasses  was  conducive 
to  the  development  of  the  latter. 

Hypermetropes  generally  prefer  a  great  distance  for  work  in  order 
not  to  fatigue  their  accommodation.  But,  when  the  hypermetropia  is 
very  high,  which  demands  an  effort  of  accommodation  much  too 
fatiguing,  we  see  patients  choose  a  very  short  distance,  moving  the 
book  to  within  a  few  centimeters  from  the  eyes.  They  see  better,  thanks 
to  the  considerable  enlargement  of  the  retinal  images.  It  is  true  that 
they  are  blurred;  but,  on  bringing  the  object  nearer,  the  circles  of  diffu- 
sion increase  less  quickly  than  the  images,  and  moreover,  the  patients 
can  diminish  them  by  winking  their  eyelids. 


92  PHYSIOLOGIC  OPTICS 

The  rule  of  Donders  for  the  selection  of  spectacles  was  to  correct  the 
manifest  hypermetropia  plus  one-fourth  of  the  latent,  that  is  to  say,  to 
give,  for  young  people,  convex  glasses  a  little  stronger  than  those 
which  they  accept  for  distant  vision.  I  consider  this  rule  a  wise  one; 
others  correct  all  the  hypermetropia.  Generally  the  patients  are  dis- 
satisfied at  the  beginning,  before  becoming  accustomed  to  the  spec- 
tacles; the  glasses  annoy  them,  and  it  is  advisable  to  forewarn  them 
that  they  will  do  so  for  some  time.  This  annoyance  is  greater  the 
stronger  the  glasses,  which  is  one  reason  for  not  correcting  all  the 
hypermetropia.  Another  reason  is  that  patients  are  much  more  annoyed 
when,  for  one  reason  or  another,  they  cannot  wear  the  glasses,  since 
they  have  lost  the  habit  of  overcoming  their  hypermetropia  by  accom- 
modation. 

If  the  hypermetropia  is  low  or  medium  (i  to  3  D.)  there  is  no  reason 
for  giving  glasses  for  distant  vision,  at  least  to  young  people  who  easily 
correct  their  hypermetropia  by  accommodating;  we  may  leave  them 
ff ee  in  this  regard.  If  the  hypermetropia  is  high  or  if  there  is  a  tendency 
to  strabismus,  the  glasses  must  be  worn  constantly,  (i) 


49.  Aphakia.  —  It  is  very  rare  to  find  true  hypermetropia  which  ex- 
ceeds 7  D.  (see  fig.  60).  The  higher  degrees  are  met  with  only  in  aphakia 
(absence  of  the  crystalline  lens). 

The  degree  of  hypermetropia  of  the  aphakic  eye  can  be  calculated  by 
means  of  the  formula^-  -j-  -^r-  =  1.  With  the  values  of  the  simplified 
eye  we  have  Fx  =  24,  F2  =  32,  /2  =  24.7,  which  gives  /±  =  —  81.2.  The 
far  point  is  therefore  situated  at  81.2  mm.  behind  the  cornea;  the  eye 
will  be  corrected  by  a  convex  glass  of  96  millimeters  =  10.4  D.,  placed 
at  15  millimeters  in  front  of  the  cornea.  We  find,  in  fact,  that  nearly  all 
the  emmetropes  operated  on  for  cataract  are  corrected  with  a  glass  of 
from  10  to  ii  dioptrics. 

But  it  would  be  an  error  to  apply  this  number  to  the  ametropias,  and  to 
think  that  we  could  always  find  the  post-operation  refraction  by  dimin- 
ishing the  ante-operation  refraction  by  n  D.  To  find  the  correcting 
glass  for  ametropias  we  must  calculate  it  in  the  same  way  as  for  emme- 


(1)  [In  this  country  our  reasoning  upon  this  point  is  quite  different.  As  people  with  hypermetropia, 
higher  than  3D.,  accommodate  with  great  difficulty,  they  do  not  keep  it  up  very  long  at  a  time  or  some- 
times avoid  to  correct  accommodation  by  reading  very  near  with  diffuse  but  enlarged  images  as  has 
been  so  well  explained  by  the  author.  They  thus  frequently  rest  their  eyes  more  than  the  persons  with 
lower  degrees  of  H.  who  use  their  accommodation  more  constantly  and  on  that  account  show  more 
asthenopia.  At  any  rate  the  constant  correction  of  the  lower  degrees  of  hypermetropia  has  relieved 
many  cases  of  obstinate  asthenopia.]— W. 


ANOMALIES   OF  REFRACTION 


tropes.    It  is  thus  that  Dr.  Stadfeldt  has  calculated  the  following  little 
table : 


Before  \  TT  7 
operation  f 

H.  5 

H.  3 

H.  1 

E 

M.I 

M.  3 

M.  5 

M.  7 

After  )rr  15 
operation  f 

H.  13.8 

H.  12.5 

H.  11.3 

H.  10.6 

H.  10.1 

H.  8.9 

H.  7.8 

H.  6.6 

Bef°r.e  IM.Q 

operation  f 

M.  11 

M.  13 

M.  15 

M.  17 

M.  19 

M.  21 

M.  23 

M.  25 

After  )  H  5  5 
operation  ( 

H.  4.4 

H.  3.4 

H.  2.3 

H.  1.3 

H.  0.2 

M.  0.8 

M.  1.8 

M.  2.7 

Comparing  this  table  with  the  following  table  which  has  been  made  up 
from  a  series  of  results  from  operations  published  by  Pflueger,  we  see 
that  the  agreement  is  sufficiently  satisfactory. 

Before  operation  M  10  Mil  M  12  M  13  M  14  M  15  M  16  M  18  M  22 
After  H5  H  5.5  H  3.5  H  3.5  H  3.5  HI  H  2.5  M  2  M  2 

Dimmer  has  directed  attention  to  a  slight  source  of  error  in  the  ordi- 
nary examination  of  aphakics.  The  lenses  of  our  test  cases  are  biconvex, 
while  those  which  the  optician  makes  for  patients  are  generally  sphero- 
cylindrical,  the  cylindrical  surface  being  turned  towards  the  eye.  Now, 
the  optic  center  of  biconvex  lenses  is  situated  at  the  middle  of  the  lens, 
while  that  of  plano-convex  glasses  is  situated  at  the  apex  of  the  convex 
surface.  It  follows  that  the  spherical  effect  of  the  sphero-cylindrical 
glass  is  a  little  greater  than  that  of  the  biconvex  glass,  having  the  same 
focal  distance,  the  posterior  focus  being  situated  a  little  nearer  the  glass 
in  the  former  case.  The  error  may  reach  a  half  dioptry.  For  some  time 
test  cases  have  been  manufactured  in  Austria  in  which  the  strong  convex 
glasses  are  plain  on  one  side. 

Ostwalt  has  laid  stress  on  the  influence  which  the  distance  of  the  glass 
from  the  eye  exerts  on  the  power  of  sphero-cylindrical  glasses.  Suppos- 
ing, for  example,  that  an  eye  is  corrected  by  +  n  D.  with  +  3  D.  cyl., 
placed  at  15  millimeters  in  front  of  the  eye.  Such  a  glass  has,  in  one  of 
the  principal  meridians,  a  focal  distance  of  91  millimeters,  in  the  other 
of  71  millimeters.  The  far  point  of  the  eye  is  thus  found  in  one  of  the 
meridians  at  91  mm.  —  15  mm.  =  76  mm.  (13.1  D.),  in  the  other  at 
71  mm.  —  15  mm.  =  56  mm.  (17.9  D.).  Its  astigmatism  is,  therefore, 
really  4.8  D.  and  not  3  D.  As  far  as  the  subjective  examination  is  con- 
cerned this  difference  plays  no  part,  since  the  glasses  with  which  we 
examine  our  patients  are  at  the  same  distance  from  the  eye  as  those 
which  the  patient  will  wear,  but  it  is  not  so  with  the  ophthalmometer, 


94  PHYSIOLOGIC  OPTICS 

which  tells  the  true  astigmatism  of  the  eye;  we  must  recollect,  there- 
fore, that  in  this  case  the  number  furnished  by  the  ophthalmometer  is 
higher  than  that  which  suits  the  patient.  —  In  the  case  of  simple  cylin- 
drical glasses  the  same  influence  makes  itself  felt,  but  to  a  much  less 
extent ;  a  convex  cylinder  of  6  D.  thus  corresponds  with  a  true  astigma- 
tism of  6.5  D.,  a  concave  cylinder  of  6  D.  with  5.5  D. 

Bibliography. — Donders  (F.  C.).  On  the  Anomalies  of  Accommodation  and  Refraction  (>f 
the  Eye.  London,  1864.  —  Mauthner  (L.).  Vorlesungen  iiber  die  optischen  Fehler  des  Auges. 
Wien,  1876.  —  Landolt  (E.).  La  refraction  et  V accommodation  de  V<x,il  in  Wecker  and  Lan- 
dolt.  Traite  complet  d'ophtalmologie.  Paris,  1883.  —  Boehra  (L.).  Das  Schielen.  Berlin,  1845. 
—  Arlt  (F.).  Die  Krankhciten  des  Auges,  I-III.  Prag.,  1851.  —  Stellwag  v.  Carion.  Die 
Ophthalmologie  vom  nitwwissenschaftlich<n  Standpunktc  aus.  I-II.  Erlargen,  1853.  — Tscher- 
ning  (M.),  Studien  iiber  die  Aetiologie  der  Myopie.  Arch.  f.  Ophfh.,  XXIX,  I,  1883.  —  Dim- 
mer (F.).  Zur  Glaesercorrection  bei  Aphakie.  Kl.  M.  f.  A.  1891.  —  Ostwalt  (F.).  Einige 
Worte  uber  Glasercorrection  bei  Aphakie.  Kl.  \f.  f.  A.  1891.  —  Demicheri  (L.).  Faux  knti- 
cone.  Ann.  d'oc.  1895. 


CHAPTER  VII. 
SPHERICAL  ABERRATION. 

50.  Optic  Principles.  —  When  the  aperture  of  a  spherical  lens  is  not 
very  small,  the  rays  proceeding  from  a  point  of  the  object  do  not, 
after  refraction,  reunite  exactly  at  a  point,  as  would  be  essential  to  form 
a  good  image;  the  borders  of  the  lens  are  more  refracting  than  the 
center.  Thus  the  test  case  lens,  the  center  of  which  has  a  refraction  of 
20  D.,  refracts  25  D.  towards  the  borders.  Generally  speaking,  the  same 
is  true  of  all  refracting  and  reflecting  systems  (fig.  61).  It  is  possible, 


Fig.  61.  —  Refraction  of  a  pencil  of  parallel  rays  by  a  spherical  surface.  Spherical  aberra- 
tion. At  A,  the  rays  are  condensed  towards  the  border  ;  at  B,  towards  the  axis  of  th 
pencil ;  p,  q,  two  needles. 

nevertheless,  to  construct  systems  of  large  aperture,  which  present  only 
very  little  aberration  (aplanatic  lenses),  and  others  in  which  the  aberra- 
tion is  over-corrected,  the  borders  being  less  refracting  than  the  center 
(lentilles  suraplanetisees) . 

The  degree  of  aberration  increases  as  the  square  of  the  aperture  of 
the  lens  and  as  the  cube  of  its  refracting  power.  It  depends,  besides,  on 
the  distance  of  the  object  and  the  form  of  the  lens.  A  plano-convex 
lens  presents  less  aberration  than  a  bi-convex  lens,  if  the  spherical  side 
is  turned  towards  the  incident  rays  supposed  to  be  parallel ;  it  presents 

95 


96  PHYSIOLOGIC  OPTICS 

more  in  the  contrary  direction.  It  is  for  this  reason  that  the  objectives 
of  opera  glasses  are  bulged  in  front.  The  best  form  of  simple  lens  is  that 
which  the  English  call  crossed  lens  (periscopic),  in  which  the  radius  of  the 
posterior  surface  is  about  six  times  greater  than  that  of  the  anterior 
surface.  We  give  here  the  refracting  power,  at  15  millimeters  from  the 
axis,  of  different  lenses,  all  having  at  the  middle  a  refraction  of  20  D. 
The  incident  rays  are  supposed  to  be  parallel. 

Crossed  lens.  Plano-convex  with  the  Bi-convex.  Plano-convex  wi*h  the 

convex  surface  in  frout.  plane  surface  in  front. 

ifl.l  D.  22.3  D.  23.6  D.  23.8  D. 

It  is  evident  that,  the  weaker  the  aberration  of  the  lens,  the  more 
aperture  can  be  given  to  it  without  the  aberration  interfering  with  the 
distinctness  of  the  image.  The  crossed  lens  is  little  used,  because  the 
plano-convex  lens  is  nearly  as  good.  Besides,  for  the  correction  of 
chromatic  aberration,  compound  lenses  are  usually  employed  (a  Hint  lens 
and  a  crown  lens  cemented  together).  Both  glasses  can  then  be  cut  in 
such  a  way  as  to  neutralize  the  spherical  aberration  also,  until  the  total 
aberration  becomes  almost  nothing  for  a  given  distance  of  the  object. 

51.  Phenomena  Dependent  on  the  Spherical  Aberration  of  Lenses.  —  I  am 
going  to  explain  some  experiments  by  which  the  spherical  aberration  of 
lenses  may  be  studied.  In  order  to  have  very  marked  phenomena  we 
must  use  a  strong  lens,  20  D.  (convex)  of  the  test-case,  for  example,  or, 
better  still,  a  strong  plano-convex  lens  (the  objective  of  an  opera  glass), 
the  plane  side  of  which  is  turned  towards  the  luminous  source,  placed 
at  a  great  distance. 

a.  APPLICATION  OF  THE  PRINCIPLE  OF  SCHEINER.  —  We  place  on  the 
lens  an  opaque  screen  in  which  we  have  previously  made,  not  two  aper- 
tures as  in  the  experiment  of  Scheiner,  but  four,  which  are  equidistant, 
placed  on  the  horizontal  diameter  of  the  lens,  two  central  ones,  2  and  3, 
and  two  peripheral,  I  and  4  (fig.  62).  The  object  being  a  distant  luminous 
source,  we  receive  the  images  on  a  white  screen  placed  behind  the  lens. 
First,  placing  the  latter  beyond  the  focus,  we  see  (fig.  62  A)  four  luminous 
spots  which  correspond  to  the  apertures  of  the  screen,  but  which  are 
placed  in  reverse  order.  The  distance  between  the  central  spots  is  less 
than  that  which  separates  each  of  the  peripheral  spots  from  the  neigh- 
boring spot.  The  two  central  spots  reproduce  the  form  of  the  source 
enlarged,  while  the  two  peripheral  spots  are  elongated  in  the  horizontal 
direction,  especially  if  the  aberration  is  strong.  The  pencils  passing 
through  the  peripheral  openings  are,  indeed,  astigmatic  by  incidence  (see 


SPHERICAL  ABERRATION 


97 


ch.  IX).  By  moving  the  screen  nearer,  the  two  central  spots  are  blended 
into  one  (fig.  62  B).  At  this  moment  the  screen  is  at  the  focus  of  the 
central  part  of  the  lens,  while  it  is  still  beyond  the  focus  of  the  peripheral 


*  K 


Fig.  62. — Spherical  aberration  of  a  lens. 

parts.  Advancing  the  screen  still  more,  the  spots  I  and  4  approach  and 
are  blended  (fig.  62  E,  focus  of  the  peripheral  part),  while  spots  2  and  3 
are  again  separated.  Finally  we  have  four  spots,  as  at  the  beginning 
of  the  experiment ;  but  they  are  now  arranged  in  the  same  order  as  the 
apertures ;  the  distances  separating  the  two  spots  on  each  side  are  less 
than  the  distance  between  the  central  spots.  We  observe  also  that  the 
peripheral  spots  are  now  elongated  in  the  vertical  direction.  —  If  the 
lens  is  very  large  we  can  observe  all  the  different  phases  shown  on 
fig.  62. 


98 


PHYSIOLOGIC  OPTICS 


To  determine  the  degree  of  aberration,  we  have  only  to  measure  the 
distances  of  the  positions  E  (focus  of  the  peripheral  parts)  and  B  (focus 
of  the  central  part)  from  the  screen.  The  difference  between  these  two 
distances,  expressed  in  dioptrics,  tells  the  degree  of  aberration.  To  have 
more  accurate  measurements  it  is  advisable  to  cover,  each  time,  the  two 
apertures  we  are  not  using;  for  the  determination  of  E,  we  cover  the 
central  apertures,  for  that  of  B  the  peripheral  apertures.  —  We  can  also 
cover  the  two  apertures  situated  on  the  same  side  and  determine  the 
focal  distance  on  the  other  side  (the  position  F,  fig.  62),  but  it  is  not 
necessary  in  order  to  determine  the  course  of  the  rays :  we  can,  indeed, 
construct  figure  62  by  knowing  the  positions  B  and  E  only. 

b.  EXAMINATION  OF  THE  CIRCLES  OF  DIFFUSION.  —  Examining  the 
circle  of  diffusion,  without  putting  the  screen  with  the  openings  on 
the  lens,  we  see  that  as  long  as  the  white  screen  is  situated  beyond  the 
focus,  the  light  is  concentrated  at  the  middle  of  the  circle ;  the  brightness 
diminishes  rapidly  towards  the  borders.    When  it  is  situated  within  the 
focus,  we  see,  on  the  contrary,  a  luminous  disc  surrounded  by  a  more 
brilliant  circle.    This  phenomenon  is  easy  to  understand :  we  see,  in  fact, 
in  figure  62,  that  the  rays  are  condensed  towards  the  border,  between 
the  lens  and  the  focus,  while  they  are  concentrated  around  the  axis 
beyond  the  focus. 

c.  DEFORMITY  OF  THE  SHADOWS.  —  Put  the  white  screen  beyond  the 
focus,  and  place  a  knitting  needle  against  the  lens.    We  then  see  the 
shadow  of  the  needle  in  the  circle  of  diffusion  and  observe  that  this 


n 


in 


Fig.  63.  —  Deformation  of  the  shadows  of  the  needles.  Successive  sections  of  the  pencil 
of  figure  61.  Section  I  is  supposed  to  be  made  at  C  (fig.  61),  section  II  at  A,  section  III 
at  B,  the  two  latter  enlarged ;  ab}  a  needle ;  a'  V  and  a"  b",  its  shadows. 

shadow  is  straight  only  if  the  needle  coincides  with  a  diameter  of  the 
lens;  otherwise  it  is  curved,  with  its  convexity  towards  the  center.  If 
the  screen  is  between  the  focus  and  the  lens,  the  shadow  is  concave 
towards  the  middle,  but  the  curvature  is  much  less  pronounced. 


SPHERICAL  ABERRATION  99 

To  understand  these  deformities  let  us  suppose  the  lens  divided  into 
concentric  zones  of  the  same  width.  A  glance  at  figure  62  shows  that 
after  refraction  the  corresponding  zones  of  the  circle  of  diffusion 
diminish  in  width  towards  the  periphery,  when  the  screen  is  situated 
between  the  focus  and  the  lens,  while  they  increase  in  width  towards  the 
periphery  beyond  the  focus.  In  figure  63,  I  shows  the  lens  seen  from 
the  front  and  divided  into  concentric  circles ;  the  two  straight  lines  rep- 
resent two  needles.  In  figure  63,  n  represents  a  circle  of  diffusion 
between  the  lens  and  the  focus.  We  see  that  the  zones  become  narrower 
towards  the  edge,  and  we  understand  that  the  point  a'  is  relatively  nearer 
the  center  than  the  point  b',  which  gives  the  shadow  its  curved  form. 
Knowing  the  position  of  the  concentric  circles  of  the  diffusion  spots, 
it  is  easy  to  construct  the  form  of  the  shadow,  since  the  shadow  of  a 
point  of  the  needle  must  be  at  the  same  angular  distance  from  the 
horizontal  diameter  as  the  point  itself.  In  figure  63,  in  represents  a 
circle  of  diffusion  beyond  the  focus. 

An  over-corrected  lens  gives  all  the  phenomena  here  mentioned,  but 
in  the  reverse  order,  while  a  corrected  lens  (aplanatic)  gives  none  of 
them.  The  circles  of  diffusion  of  an  aplanatic  lens  have  the  same  bright- 
ness in  their  whole  extent,  and  the  shadow  of  the  needle  remains 
straight  everywhere.  To  give  a  good  image  a  lens  must  be  approx- 
imately aplanatic.  The  preceding  experiments  can  be  used  as  a  verifica- 
tion of  the  aplanatism  of  a  lens. 

d.  APPLICATION  OF  THE  PRINCIPLE  OF  FOUCAULT.  —  We  obtain  very 
pretty  phenomena  by  using  the  method  by  which  Foucault  studied  his 
telescopes.  We  place  a  luminous  point  a  little  beyond  the  focus  of  the 
lens  which  we  wish  to  study,  so  that  its  image  is  quite  distant  (2  to  3 
meters).  The  observer  takes  his  place  beyond  this  image,  so  that  his 
eye  is  in  the  luminous  pencil  on  the  axis  of  the  lens,  which  he  approaches 
gradually.  Under  these  circumstances  the  eye  sees  luminous  the  parts 
of  the  lens  which  send  rays  to  it.  If  the  lens  were  aplanatic,  all  the  rays 
would  meet  at  the  focus,  and,  reaching  this  point,  the  observer  ought 
to  see  the  entire  lens  luminous.  At  some  distance  from  the  focus,  he 
would  see,  on  the  contrary,  only  a  small  central  part  luminous,  the  other 
rays  not  entering  his  eye.  If  the  lens  is  affected  with  spherical  aberra- 
tion, we  observe  the  following  phenomena :  placed  very  far  off  we  see 
only  a  quite  small  central  spot,  which  increases  in  diameter  accordingly 
as  we  approach  the  focus  where  it  attains  its  maximum ;  but  even  here  it 
is  far  from  filling  the  entire  lens.  Approaching  still  nearer  we  see  a 
luminous  ring  become  detached  and  separated  from  the  central  part  by 


100  PHYSIOLOGIC  OPTICS 

a  dark  zone.  This  ring  dilates  more  and  more  accordingly  as  we  ap- 
proach the  lens,  while  the  dark  zone  becomes  enlarged.  On  reaching 
a  certain  point,  the  ring  extends  to  the  borders  of  the  lens  and  disap- 
pears. The  phenomena  are  still  clearer  if  we  look  through  a  narrow 
diaphragm.  —  It  is  easy  to  account  for  the  nature  of  these  phenomena 
by  glancing  at  figures  61  and  62.  Thus,  if  we  suppose  the  pupil  of  the 
observer  reduced  to  a  point  and  placed  at  the  intersection  E,  fig.  62,  it 
would  receive  rays  I  and  4,  and  the  borders  of  the  lens  would  appear 
luminous,  while  the  parts  2  and  3  would  be  black,  the  corresponding 
rays  passing  to  one  side  of  the  pupil.  There  will  always  be  a  small, 
luminous  spot  at  the  middle,  since  the  axial  ray  always  enters  the  eye. 
The  distance,  in  dioptrics,  between  the  place  where  the  ring  appears 
and  that  where  it  disappears,  tells  the  amount  of  the  aberration.  —  If 
the  aberration  is  over-corrected  we  have  the  same  phenomena  in  the 
reverse  order :  placed  at  the  focus,  we  must  move  away  in  order  to  see 
the  ring;  the  further  away  we  move  the  more  it  increases,  until  finally 
it  disappears. 

52.  Aberration  of  the  Human  Eye.  Experiments  of  Volkmann.  —  This 
scientist  examined  the  aberration  of  the  eye  by  repeating  the  experiment 

of  Schemer  with  four  openings 
located  as  indicated  in  figure 
64,  C.  Looking  at  a  pin  placed 
beyond  the  far  point  through 
these  openings,  it  is  seen 
quadrupled  (fig.  64,  A,  a) ;  and 
by  moving  closer  to  it  he  ob- 
*  °  *  *  served  the  different  phases 

c    ••  illustrated  in  figure  64,  A,  in 

the  order  in  which  they  are 

Fig.  64.  —  Experiment  of  Volkmann. —  o,  corre-         ,  .     A1       -  .      ..  . 

spends  to  the  most  distant  position ;  e,  to  the      shown  in  the  figure,  and  which 

nearest  position  of  the  needle.  A  phenomena       corresponds    to    the    spherical 

observed  by  an  eye  with  strong  spherical  aber-  r 

ration ;  B,  by  an  eye  with  over-corrected  aber-       aberration.      It  IS   easy  to  ac- 

count  for  this  phenomenon  by 

comparing  figure  64  with  figure  62.  In  the  position  b,  the  pin  is  at  the 
far  point  of  the  central  parts  of  the  pupil,  since  the  two  central  images 
are  reunited ;  it  is  still  beyond  the  focus  of  the  peripheral  parts  since  the 
peripheral  images  are  not  yet  blended.  Most  of  the  time,  the  persons 
examined  observe  the  same  phenomena  in  the  same  order,  but  some  see 
them  in  the  reverse  order  (fig.  64,  B),  which  indicates  over-corrected 


m 


t  n  i  in 


SPHERICAL  ABERRATION  101 

aberration.  In  the  position  d  (fig.  64,  B)  the  pin  is  at  the  far  point  of  the 
central  parts  and  within  the  far  point  of  the  peripheral  parts.  —  It  is 
probable  that  these  latter  persons  used  their  accommodation,  for  it  is 
quite  rare  to  find  over-corrected  aberration  in  an  eye  in  a  state  of  repose ; 
I  have,  however,  met  instances,  especially  among  persons  having  a  large 
pupil.  On  the  contrary,  during  accommodation,  it  is  the  rule  that  the 
aberration  is  over-corrected,  as  we  shall  see  later  on. 

53.  Experiments  of  Thomas  Young.  —  Long  before  V 'olkmanri 's  time, 
Young  had  already  performed  a  series  of  experiments  much  more  con- 
clusive, but  which  had  been  forgotten. 

a.  A  myopic  eye  sees  a  distant  luminous  point  as  a  circle  of  diffusion, 
the  brightness  of  which  is  concentrated  at  the  middle,  if  the  eye  has 


I  II 

Fig.  65.  —  Distribution  of  the  light  of  the  circle  of  diffusion  in  an  eye  with  strong  aberra- 
tion (Antonelli).   In  I  the  luminous  point  is  beyond;  in  II  within  the  focus. 

spherical  aberration  (fig.  65,  I).  If  the  aberration  is  over-corrected,  or 
if  the  luminous  point  is  inside  the  far  point,  it  is  the  borders  that  are 
the  more  luminous;  an  aplanatic  eye,  or  one  nearly  so,  sees  the  circle 
of  a  uniform  brightness.  To  repeat  the  experiment,  when  one  is  not 
myopic,  one  places  in  front  of  the  eye  a  convex  lens  of  3  to  4  dioptrics. 
Many  eyes,  the  optic  system  of  which  is  irregular,  perceive  eccentric 
concentrations  of  the  light;  I  shall  return  to  this  immediately,  (i) 

b.  Bringing  a  needle  in  front  of  the  eye,  made  myopic,  while  the  ex- 
periment a  is  being  performed,  we  see  the  shadow  of  the  needle  in  the 
circle  of  diffusion.  If  the  shadow  remains  straight  everywhere,  there  is 


(1)  Young  does  not  mention  the  experiment  under  this  form,  but  it  is  a  sequence  of  other  expert 
ments  which  he  describes.  For  the  experiment  6,  he  used  the  bars  separating  the  four  slits  of  his  opto- 
meter. 


102 


PHYSIOLOGIC  OPTICS 


no  perceptible  aberration;  if  it  is  curved,  its  concavity  towards  the  pe- 
riphery indicates  ordinary  aberration ;  its  concavity  towards  the  center 
indicates  over-corrected  aberration.  We  can  perform  the  experiment  in 

the  different  meridians  and  thus  prove  that  the 
aberration  is  not  always  the  same  in  the  differ- 
ent directions. 

I  have  constructed  a  little  instrument,  the 
aberroscope  (fig.  66),  consisting  of  a  plano-con- 
vex lens  which,  on  its  plain  side,  carries  a 
micrometer  in  the  form  of  little  squares.  We 
look  at  a  distant  luminous  point  through  the 
lens,  moving  it  10  or  20  centimeters  from 


Fig.  66.  —  The  aberroscope. 


Fig.  67.  —  The  rules  of  the  optometer  of  Young. 


the  eye  in  order  to  observe  whether  the  lines  then  appear  curved 
or  not. 

c.  THE  OPTOMETER  OF  YOUNG  enables  us  to  measure  spherical  aberra- 
tion directly.  In  the  horizontal  rule  (fig.  67),  on  the  left,  are  two  slits, 
very  narrow  and  very  close.  We  look  at  the  line  through  these  slits 
and  determine  the  central  refraction  by  observing  the  intersection  of  the 
two  apparent  lines,  as  I  have  explained  in  chapter  V.  Care  must  be 
taken  to  place  the  slits  so  that  both  the  lines  appear  of  the  same  dis- 
tinctness, which  takes  place  when  the  slits  are  almost  at  the  middle  of 
the  pupil.  This  done,  we  bring  the  quadrangular  aperture  in  front  of 
the  lens,  and  gradually  lower  the  vertical  rule  which  has  the  triangular 


SPHERICAL  ABERRATION 


103 


plate,  so  as  to  exclude  a  continually  increasing  part  of  the  middle  of 
pupil.  We  then  see  two  intersecting  lines  which  separate  more  and 
more,  until  one  of  them  disappears  at  the  moment  when  the  width  of 
the  plate  is  equal  to  the  diameter  of  the  pupil.  We  then  raise  the  rule  a 
little,  so  as  to  again  see  two  lines,  and  measure  the  refraction.  The 
difference  between  this  measurement  and  that  made  with  the  two  slits 
placed  at  the  center  indicates  the  degree  of  aberration. 


00 

J  II  III 

Fig.  68.  —  I  and  II.  The  appearance  assumed  by  the  line  »f  the  optometer  of  Young,  seen 
through  four  slits  by  one  eye  with  strong  spherical  aberration.  O,  position  of  the  eye ; 
a  (a')  far  point  of  the  peripheral  parts ;  b  (&')  far  point  of  the  central  parts. 

III.  The  appearance  of  the  line,  seen  in  the  same  circumstances  by  one  eye  (left) 
with  marked  obliquity.  The  external  part  of  the  pupillary  space  is  more  refracting 
than  the  internal  part. 

Young  made  two  measurements  at  once  by  using  four  slits  of  the 
horizontal  rule.  The  experiment  thus  performed  is  much  more  elegant 
and  sure,  but  it  is  often  difficult  to  succeed,  especially  if  the  pupil  is  not 
dilated.  It  is  easier  to  succeed  if  the  slits  are  brought  together  in  pairs, 


104  PHYSIOLOGIC  OPTICS 

leaving  a  central  interval  a  little  greater  than  that  between  the  pairs.  — 
With  the  four  slits  we  see  four  lines  (fig.  68,  I);  if  there  is  spherical 
aberration  the  two  central  lines  intersect  farther  away  (at  b)  than  the 
peripheral  lines  (a).  Very  frequently  the  lines  partly  blend,  so  as  to 
give  the  appearance  shown  in  figure  68,  II.  Figure  68,  III,  shows  the 
appearance  which  the  line  assumes  to  an  unsymmetrical  eye  (left),  the 
external  part  of  the  pupil  being  more  refracting  than  the  internal. 

We  can  also  measure  with  the  two  slits  the  refraction  at  the  middle 
of  the  pupil,  as  we  did  just  before,  and  then  displace  the  slits  successively 
towards  either  border  until  one  of  the  lines  begins  to  disappear.  We 
thus  determine  the  refraction  near  the  two  borders.  This  experiment, 
by  which  we  determine  the  position  of  the  point  r,  figure  68,  I,  is 
analogous  to  that  described  on  page  98,  in  which  we  covered  the  two 
apertures  situated  on  the  same  side  of  the  lens  to  measure  the  refraction 
on  the  other  side.  The  measurements  made  with  the  slits  placed  pe- 
ripherally generally  differ  more  from  those  obtained  with  the  central 
slits  than  do  the  measurements  made  with  the  triangular  plate,  which  is 
so  also  in  the  case  of  the  lens. 

SKIASCOPIC  EXAMINATION.  —  While  the  methods  which  we  have  just 
mentioned  are  quite  delicate,  skiascopy  furnishes  us  with  a  convenient 
means  of  examining  the  aberration  of  the  human  eye.  For  this  pur- 
pose it  is  necessary  to  use  skiascopy  with  a  luminous  point,  a  method  which 
has  been  with  good  cause  recommended  by  Jackson,  and  which  is  nothing 
more  than  an  application  of  the  principle  of  Foucault.  We  observe  the 
pupil,  while  we  form  a  distinct  image  of  a  luminous  point  on  the  retina. 
We  surround  a  flame  with  an  opaque  tube  pierced  with  an  opening  of 
one  centimeter  diameter;  it  is  the  image  of  this  opening  that  we  project 
on  the  retina  with  an  ophthalmoscope,  and  care  must  be  taken  in  select- 
ing the  mirror  so  that  this  image  may  be  distinct;  in  other  words,  so 
that  the  image  of  the  opening  formed  by  the  mirror  is  near  the  place 
for  which  the  observed  eye  is  focused.  If  the  observed  person  is  emme- 
tropic,  we  place  the  light  at  50  centimeters  or  one  meter  behind  him, 
and  examine  with  a  plane  mirror.  If  he  is  myopic,  we  use,  on  the  con- 
trary, a  concave  mirror  which  projects  the  image  of  the  luminous  point 
near  his  far  point.  In  all  cases  it  is  advisable  that  the  opening  of  the 
mirror  be  quite  small,  about  2  mm.  The  pupil  of  the  observed  person 
must  be  dilated. 

To  examine  the  aberration,  we  make  the  observed  person  emmetropic, 
and,  placing  ourselves  at  50  centimeters  distance,  we  project  a  light  on 
the  eye.  Generally  we  will  see  at  once  the  phenomenon  of  aberration : 


SPHERICAL  ABERRATION  105 

the  borders  of  the  pupil  are  luminous,  separated  from  the  central  light 
by  a  dark  zone.  We  approach  until  the  ring  disappears;  if  this  takes 
place  at  25  centimeters  from  the  observed  person,  the  aberration  is 
positive  and  4  D.  If  we  do  not  perceive  the  ring,  we  move  back  as  far 
as  one  meter;  if  it  does  not  yet  appear,  we  try  whether  the  aberration 
is  over-corrected :  we  make  the  observed  person  myopic  3  D. ;  if  the 
ring  appears,  we  increase  the  myopia  until  it  disappears.  If  it  disap- 
pears with  myopia  of  4  D.,  the  aberration  is  —  2  D.,  since  we  must  take 
off  2  D.,  the  observer  being  at  50  centimeters.  Brudze^vsk^,  who  de- 
termined the  aberration  of  a  certain  number  of  persons  in  this  way, 
said  that  it  is  rare  not  to  meet  with  positive  aberration  in  some  part  of 
the  pupil.  It  happens,  indeed,  quite  often  that  the  ring  is  incomplete, 
or  even  that  there  remains  only  a  very  small  section  of  it.  Negative 
aberration  is  met  with  most  frequently  inwards  or  upwards  in  the  pupil 
where  the  corneal  flattening  begins  soonest. 

RESULTS.  —  Examined  with  the  aberroscope  most  people  indicate  a 
certain  degree  of  aberration,  which  corresponds  closely  to  the  nearly 
spherical  (toric)  form  of  the  optic  part  of  the  cornea  (fig.  69).  —  Since 


I  II 

Fig.  69.  —  Deformity  of  the  shadows  in  an  eye  with  strong  spherical  aberration  (Anto- 
nelli).  I,  in  a  state  of  repose;  II,  during  accommodation.  In  the  latter  case  the  aber- 
ration is  nearly  corrected. 

the  peripheral  parts  of  a  spherical  surface  are  too  refracting,  we  can 
correct  the  defect  by  flattening  it  towards  the  periphery.  We  also  some- 
times find  people  whose  aberration  is  corrected,  or  even  over-corrected, 
towards  the  borders,  where  the  basilar  part  of  the  cornea  comes  into 
play  (fig.  70).  And,  if  the  pupil  is  placed  a  little  eccentrically,  we  may 
thus  find  aberration  in  one  direction  and  over-corrected  aberration  in 
another  (fig.  71).  Thus  the  middle  of  my  pupil  is  slightly  myopic  and 


106 


PHYSIOLOGIC   OPTICS 


the  upper  part  slightly  hypermetropic,  while  the  lower  marginal  part 
measures  a  myopia  of  three  dioptrics,  which  may  even  reach  four  diop- 
trics when  the  pupil  is  dilated.  I  have,  therefore,  spherical  aberration 
below  (and  on  both  sides),  over-corrected  aberration  above.  —  One  of 
my  friends,  who  is  an  astronomer,  has  aberration  in  the  vertical  meri- 
dian, while  the  horizontal  meridian  is  corrected. 

Some  are  met  with  who  have  slightly  over-corrected  aberration  in 
the  entire  pupillary  space  (fig.  72).  These  are  probably  persons  in  whom 
the  spherical  part  of  the  cornea  is  of  little  extent.  —  The  ophthalmo 


.  70.  —  Aberration  over-       Fig.  71.  —  Aberration  over-     Fig.  72.  —  Aberration  over- 
corrected  towards  the  borders.  corrected  above.  corrected  every  where. 


metric  measurements  of  Brudzewski,  which  I  have  mentioned,  page  59, 
enable  us  to  calculate  directly  the  degree  of  the  aberration  of  the  cornea. 
They  show  that  there  exist,  in  this  regard,  considerable  variations. 
Corneal  aberration  is,  as  a  rule,  positive,  negative  aberration  being 
rather  an  exception.  Positive  aberration  is  especially  pronounced  in 
cases  of  corneas  of  great  curvature,  which  is  not  surprising,  since  the 
aberration  increases  in  very  close  proportion  to  the  central  refraction. 
Negative  aberration  is  met  with  most  frequently  on  the  inner  side,  some- 
times above  or  below,  very  rarely  outside.  The  greatest  degree  of 
aberration  which  Brudzewski  found  was  4-  4.5  (temporal  side),  the  least 
—  2.2  D.  (nasal  side).  Generally  it  varied  between  +  3  and  —  1.5.  The 
numbers  are  calculated  for  a  distance  of  4  mm.,  starting  from  the  axis ; 
they  correspond,  therefore,  to  a  maximum  dilation  of  the  pupil ;  the 
values  diminish  as  we  approach  the  axis. 

Stadfeldt  measured  the  aberration  of  the  dead  crystalline  lens  by  the 


SPHERICAL  ABERRATION 


107 


ID" 


method  of  Foucault.    When  the  crystalline  lens  was  taken  from  the  eye, 

in  its  capsule  and  with  the 
zonula,  he  fixed  it  in  a  cork  ring 
which  he  then  placed  in  a  small 
tube  filled  with  serum  and  closed 
in  front  and  behind  by  plane 
parallel  plates  of  glass.  He 
placed  this  tube  on  the  support 
A  (fig.  720),  which  moved  along 
the  graduated  rule  E  D.  The 
lens  C  concentrated  the  light  of 
a  flame  on  a  very  fine  opening 
pierced  in  the  screen  B  D.  The 
crystalline  lens  was  observed 
with  a  telescope,  placed  at  some 
distance  in  the  direction  K;  an 


Fig.  72a.  —  StadfeldCs  instrument  for  measur- 
ing the  aberration  of  the  crystalline  lens 
(dead). 


ocular  micrometer  permitted  the  measurement  of  the  diameter  of  the 
aberration  ring,  corresponding  to  a  given  distance  between  A  and  the 
plate  B  D.  —  The  determination  of  the  focal  distance  of  the  central 
part  is  less  exact  by  this  method.  To  have  a  more  exact  measurement, 
Stadfeldt  removed  the  plate  B  D,  and  placed  a  microscope  of  slight 
magnifying  power  in  the  tube  K.  He  then  sighted  towards  an  object 
placed  at  a  great  distance.  By  displacing  the  cursor  A,  leaving  the 
microscope  motionless,  he  put  the  latter  in  focus,  first  for  the  image 
of  the  distant  object  formed  by  the  crystalline  lens,  and  then  for  the 
posterior  surface  of  the  crystalline  lens  itself.  The  difference  between 
the  two  positions  of  the  cursor  A  enabled  him  to  calculate  the  focal  dis- 
tance of  the  crystalline  lens. 

By  these  methods  Stadfeldt  proved  that  a  central  part  of  the  crystal- 
line lens  (up  to  a  distance  of  2  mm.  from  the  axis)  may  be  considered 
as  aplanatic.  This  part  is  surrounded  with  a  zone  (up  to  3.5  mm.  from 
the  axis),  the  aberration  of  which  is  over-corrected  (about  2  D.).  Very 
close  to  the  borders  the  aberration  changes  sign  and  becomes  positive. 
The  over-correction  is  due  to  the  diminution  of  the  index  towards  the 
periphery,  but  very  close  to  the  borders  the  increase  of  curvature  of  the 
surface  is  so  great  that  the  diminution  of  the  index  is  not  sufficient  to 
correct  the  aberration. 

Although  aberration  may  sometimes  be  very  pronounced,  it  does 
not  seem  to  hurt  the  visual  acuity  much  as  long  as  it  continues  entirely 
regular,  a  remark  which  Graefe  made  on  the  occasion  of  his  celebrated 


108  PHYSIOLOGIC  OPTICS 

case  of  aniridia.  The  reason  is  that  patients  do  not  use  the  part  of 
the  cone  of  which  the  diameter  is  smallest,  but  another  part  near  B, 
figure  61.  Placing  a  screen  at  this  place,  the  image  of  a  point  is  pre- 
sented as  a  point  surrounded  with  a  slightly  luminous  halo;  if  the 
brightness  of  the  object  is  feeble,  as  is  most  frequently  the  case  in  the 
ordinary  circumstances  of  life,  this  halo  is  too  slight  to  be  perceived, 
and  the  image  becomes  quite  good.  —  We  see  (fig.  61)  that  a  section  of 
the  caustic  (the  most  luminous  part  of  the  cone)  has  the  form  of  the 
head  of  an  arrow.  The  point  of  the  arrow  is  directed  backwards  in  eyes 
with  ordinary  aberration  and  forwards  in  those  with  over-corrected 
aberration ;  it  corresponds  to  the  focus  of  the  central  rays,  and  it  is  this 
point  which  serves  for  vision;  but,  as  it  is  very  pointed,  it  follows  that 
the  determination  of  the  refraction  cannot  be  of  very  great  exactness. 
The  spherical  aberration  acts,  in  this  regard,  as  a  narrow  diaphragm. 
If  a  lens  is  diaphragmed  much  it  becomes  very  difficult  to  determine  its 
focus  exactly.  —  Thanks  to  this  form  of  the  caustic,  very  regular  eyes 
can  have  a  very  beautiful  visual  acuity  despite  a  strong  aberration ;  but, 
in  most  eyes,  the  refraction  is  irregular,  so  that  patients  have  not  this 
advantage  (see  chapter  X).  I  think,  however,  that  they  generally  select 
the  place  where  the  section  of  the  caustic  is  smallest,  and  not  that  where 
the  cone  has  the  least  diameter. 

Bibliography.  —  OSavres  de  Th.  Young,  p.  153.  —  Volkmann  (A.  W.)  in  Wagner. 
Handworterbuch  der  Physiologic,  Art.  Sehen,  p.  292.  — Meyer  (H.).  Ueber  die  spharischcn 
Abweichungen  des  menschlichen  Auges.  Poggendorfs  Ann.  LXXXIX,  p.  540.  —  Tscherning 
(M.).  Diemonochromatischen  Abweichungen  des  menschlichen  Auges.  Zeitschr.f.  Physiol.  der  Sin- 
nesorgane,  VI,  p.  456.  —  Stadfeldt  (A.)  and  Tscherning  (M.).  Une  nouvelle  methode  pour 
etudier  la  refraction  cristaUinienne,  Arch,  de  physiol.,  July,  1896.  —  Jackson.  Skiascopy.  Phila- 
delphia, 1896.  —  Stadfeldt  (A.).  Recherches  sur  Vindice  total  du  cristaUin  humain.  Journal  de 
Physiologic,  November,  1899.  —  Brudzewski  (K.).  Beitrag  zur  Dioptrik  des  Auges.  Archiv 
ur  Augcnhcilkunde,  XL,  3. 


CHAPTER  VIII. 

CHROMATIC  ABERRATION. 

54.  Optic  Principles.  —  By  receiving  on  a  screen  a  pencil  of  white  rays 
which,  after  having  passed  through  a  slit,  has  traversed  a  prism,  we 
obtain  what  is  called  a  spectrum,  a  luminous  band  containing  the  entire 
gamut  of  the  colors  of  the  rainbow,  arranged  in  the  following  order: 
red,  orange,  yellow,  green,  blue,  violet.  Each  white  ray  is  divided  into 
colored  rays  which  are  refracted  differently,  the  red  the  least,  the  violet 
the  most,  which  we  express  by  saying  that  the  index  of  refraction  of 
the  glass  is  greater  for  the  violet.  If  we  speak  of  the  index  of  a  medium, 
without  more  particular  specification,  it  is  generally  the  index  of  the 
yellow  rays  (the  sodium  line)  that  is  meant.  —  The  difference  between 
the  index  of  the  violet  and  that  of  the  red  is  called  the  dispersion  of  the 
medium.  Instead  of  receiving  the  spectrum  on  a  screen,  we  can  observe 
it  directly  by  looking  at  the  slit  through  the  prism.  For  this  observa- 
tion the  prism  is  frequently  combined  with  an  astronomical  telescope 
(spectroscope). 

In  order  that  the  spectrum  may  be  really  pure  we  must:  i°  make  use 
of  a  very  narrow  slit ;  2°  interpose  a  lens  so  that  the  rays  of  each  color 
may  be  reunited  on  the  screen  in  a  distinct  image  of  the  slit.  The 
spectrum  is,  therefore,  in  reality  composed  of  a  whole  series  of  images 
of  the  slit;  if  these  images  are  not  distinct  they  are  partly  overlapped 
and  the  colors  are  not  pure.  —  To  obtain  a  very  great  purity  of  colors, 
special  precautions  must  be  used:  we  project  the  spectrum  on  a  screen 
pierced  by  a  slit  at  the  place  where  the  color  we  desire  to  examine  is 
formed.  Through  this  slit  an  eye  situated  behind  the  screen  receives 
the  light  of  this  color,  mixed  with  a  little  white  light,  due  to  diffusion 
in  the  substance  of  the  prism  and  lens.  To  eliminate  this  white  light, 
we  observe  the  slit  through  a  second  prism.  It  forms  a  spectrum  which 
is  very  weak  everywhere,  except  at  the  location  of  the  color  we  desire 
to  examine  (Helmholtz).  —  The  length  of  the  spectrum  depends  on  the 
size  of  the  angle  of  the  prism  and  on  the  degree  of  dispersion  of  the 

109 


110 


PHYSIOLOGIC  OPTICS 


glass:  a  prism  of  flint  glass  produces  a  spectrum  much  longer  than  a 
prism  of  crown  glass.  —  Beyond  the  red  there  are  ultra-red  rays,  which 
are  invisible,  but  which  have  a  greater  caloric  effect  than  the  visible 
rays.  Beyond  the  violet  rays  there  are  likewise  ultra-violet  rays,  which, 
in  ordinary  circumstances,  are  invisible,  but  which  act  on  photographic 
plates.  They  can  be  made  visible  by  overlaying  the  screen  with  a 
"fluorescent"  liquid  (sulphate  of  quinine,  fluorescence,  etc.).  Struck  by 
the  ultra-violet  rays,  these  substances  send  back  visible  rays,  generally 
bluish  or  greenish.  —  With  certain  precautions  we  can  see  directly  a  part 
of  the  ultra-violet  rays,  perhaps  because  the  retina  itself  is  fluorescent. 
Thus  Mascart  mentions  a  physicist  who  could  distinguish  the  lines  of 
Fraunhofer  in  the  ultra-violet  part  of  the  spectrum  as  far  as  the  photo- 
graphic plate  could  reproduce  them.  We  cannot  make  the  ultra-red 
rays  visible  because  they  do  not  pass  through  the  media  of  the  eye 
(Bruecke). 

Generally,  the  media  which  have  a  greater  index  have  also  a  greater 
dispersion,  (i)  but  the  index  and  dispersion  are  not  proportional.  Thus 
Hint  glass,  for  example,  gives  a  dispersion  nearly  double  that  of  crown 
glass,  while  its  index  is  1.7  and  that  of  crown  1.5.  —  If  we  combine  a 
prism  of  crown  glass  with  another  of  flint  glass  in  an  inverse  manner, 
the  angle  of  which  is  nearly  a  half  less,  the  dispersion  may  be  neutral- 
ized, while  there  remains  a  quite  considerable  part  of  the  refraction  of 
the  crown  glass.  Such  a  combination  constitutes  an  achromatic  prism 
(fig-  73)- 


Fig.  73.  —  Achromatic  prism. 


Fig.  74.  —  Prism  d,  vision  directe. 


We  can  also  construct  combinations  of  prisms  which  give  no  devia- 
tion to  the  emerging  ray,  but  which  have  a  quite  considerable  dispersion : 


(1)  This  assertion  is  true  for  the  glasses  which  we  generally  use,  but  not  for  the  new  glasses  manu- 
factured by  Abbe  &  Schott  at  Jena  since  1886.  They  succeeded  in  making  one  part  of  crown  glass  (with 
baryta  basis)  which  has  scarcely  any  more  dispersion  than  the  ordinary  crown  glass,  but  the  average 
index  of  which  is  equal  to  that  of  very  dense  flint,  and  another  part,  of  crown  glass,  with  low  index 
and  relatively  high  dispersion.  The  new  glasses  are  imported  for  the  manufacture  of  microscopic  ob- 
jectives (apochromatic  systems,  see  the  following  page)  and  also  for  photographic  objectives.  Under  the 
name  of  isometropic  glasses,  they  have  been  used  for  spectacle-making  purposes,  but,  in  this  respect,  they 
present  no  advantage. 


CHROMATIC  ABERRATION  111 

we  call  these  combinations  prisms  a  vision  dirccte  (fig.  74);  they  are 
much  used  for  the  construction  of  spectroscopes. 

By  passing  through  a  lens  the  colored  rays  are  also  separated.  As 
the  index  is  stronger  for  the  blue  rays  (violet),  the  blue  focus  is  nearer 
the  lens  than  the  red  focus.  This  is  the  reason  why  the  circle  of  diffusion 
of  a  convex  lens  is  bordered  with  red  inside  the  focus  and  with  blue 
beyond.  —  Lenses  may  be  made  achromatic  by  the  same  system  as 
prisms :  a  convex  lens  of  crown  glass  is  combined  with  a  concave  lens, 
half  as  strong,  of  Hint.  The  circles  of  diffusion  of  such  a  lens  no  longer 
present  red  and  blue  borders,  but  there  still  remain  traces  of  other 
colors  (green  and  purple).  Zeiss  at  Jena  caused  these  latter  to  disappear 
also  by  combining  several  glasses  of  different  kinds,  specially  manu- 
factured for  this  purpose  (apochromatic  systems). 

55.  Chromatic  Aberration  of  the  Eye.  —  The  eye  is  not  achromatic  as 
was  for  a  long  time  believed.    The  question  has  played  quite  a  curious 
part  in  the  history  of  optics.    Newton  thought  that  the  dispersion  of  a 
medium  was  proportional  to  its  index  and  that,  consequently,  the  con- 
struction' of  an  achromatic  objective  was  a  chimera;  this  is  why,  for- 
saking astronomical  telescopes,  he  adopted  catoptric  telescopes.     But 
Euler  concluded  that,  the  eye  being  achromatic,  it  must  be  possible  to 
construct  achromatic  lenses,  and  this  remark  led  Dolknd,  the  optician, 
to  construct  objectives  thus  corrected.     Later  Wollaston  demonstrated 
that  the  eye  is  not  achromatic.    This  is  not  the  only  time  that  useful 
results  have  been  arrived  at  by  starting  from  a  false  hypothesis. 

56.  Experiment  of  Wollaston.  —  A  luminous  point  seen  through  a 
prism  gives  a  linear  spectrum.    But,  making  the  experiment,  we  observe 
that  we  cannot  see  distinctly  at  once  the  entire  extent  of  the  spectrum. 
If  the  luminous  point  is  at  a  great  distance,  the  emmetropic  eye  sees 
the  red  extremity  of  the  spectrum  as  a  distinct  line,  while  the  blue  ex- 
tremity is  enlarged  and  frequently  divided  into  two  ("like  the  tail  of  a. 
swallow").    If  we  go  nearer,  taking  care  not  to  use  our  accommodation, 
we  find  a  distance  at  which  we  are  focused  for  the  blue  extremity,  while 
the  red  extremity  is,  in  turn,  diffuse.    The  observer  can,  therefore,  de- 
termine his  far  point  for  each  extremity  of  the  spectrum ;  the  difference 
gives  the  degree  of  chromatic  aberration. 

Wollaston  has  likewise  directed  attention  to  another  phenomenon  of 
chromatic  aberration:  the  colored  borders  which  are  seen  along  the 
lines  of  the  optometer  of  Young. 


11-2  PHYSIOLOGIC  OPTICS 

EXPERIMENTS  WITH  THE  COBALT  GLASS.  —  Placing  a  luminous  point, 
such  as  an  opening  in  an  opaque  screen,  inside  the  near  point,  we  see  a 
circle  of  diffusion  bordered  with  red  exactly  as  when  we  made  the 
analogous  experiment  with  the  lens ;  it  is  more  difficult  to  see  the  blue 
border  which  surrounds  the  point,  when  it  is  situated  beyond  the  far 
point.  The  experiment  is  much  more  striking  when  the  point  is  ob- 
served through  a  cobalt  glass.  These  glasses  allow  only  the  blue  and 
red  rays  to  pass;  looking  at  a  luminous  point  situated  inside  the  near 
point,  through  such  a  glass,  we  see  it  blue  and  surrounded  by  a  red 
halo.  If  the  luminous  point  is  situated  beyond  the  far  point,  we  see,  on 
the  contrary,  a  red  point  surrounded  with  blue. 

EXPERIMENTS  OF  FRAUNHOFER.  —  This  scientist  determined  the  dis- 
tance at  which  he  could  see  distinctly  a  spider  thread  placed  sometimes 
in  the  red  light,  sometimes  in  the  blue  light  of  the  spectrum.  We  thus 
obtain  very  exact  results. 

57.  Results.  —  Young  estimated  the  chromatic  aberration  of  the  eye 
at  1.3  D.,  Fraunhofer  found  1.5  to  3  D.,  Helmholts  gives  1.8  D.  The 
number  is  difficult  to  determine  exactly,  since  the  lowest  limit  of  the 
visible  spectrum  is  not  well  defined.  —  The  dispersion  of  the  eye  is  a 
little  greater  than  it  would  be  if  the  eye  were  filled  with  water. 

The  eye,  therefore,  is  not  achromatic,  and,  as  we  have  seen,  it  is  easy 
to  convince  oneself  of  it  when  the  object  is  situated  beyond  the  far  point 
or  within  the  near  point.  But  when  the  object  is  at  such  a  distance  that 
it  can  be  seen  distinctly,  we  do  not  see  colored  borders.  The  explana- 


Violet 


Fig.  75.  —  Chromatic  aberration  of  the  eye. 

tion  which  is  given  of  this  fact  is  the  following:  Let  A  (fig.  75)  be  a 
luminous  point  which  sends  the  cone  ABC  into  the  eye.  After  refraction, 
the  white  rays  are  divided  into  colored  rays ;  the  red  rays  form  the  cone 


CHROMATIC  ABERRATION  113 

BrC,  the  violet  rays,  which  are  more  refracted,  the  cone  Bz/C,  and  the 
eye  accommodates  itself  in  such  a  way  that  the  retina  is  between  the 
two  foci,  placed  so  that  the  red  diffusion  circle  covers  the  blue  one  (see 
fig-  75)-  The  intermediary  rays  of  the  spectrum,  the  yellow  and  the 
green,  which  are  the  most  luminous,  are  then  concentrated  at  the  middle 
of  the  diffusion  circle,  where  they  coincide  with  a  part  of  the  red  and  a 
part  of  the  violet,  while  the  peripheral  parts  of  the  red  and  violet  form 
a  purple  border  all  around ;  but  this  border  is  very  narrow,  and,  as  it  is 
formed  by  the  extreme  rays  of  the  spectrum,  which  are  very  slightly 
luminous,  it  is  too  weak  to  be  perceived.  —  When  observing  a  luminous 
point  with  an  astronomical  telescope,  the  objective  of  which  is  not  very 
well  achromatized,  the  same  phenomena  are  seen:  if  the  telescope  is 
focused  for  a  nearer  point,  the  circle  appears  surrounded  with  blue ;  in 
the  contrary  case  it  is  bordered  with  red,  and,  when  the  point  is  seen 
distinctly,  it  is  surrounded  by  a  very  narrow  purple  border.  —  The  same 
thing  occurs  if  the  point  A  be  replaced  by  a  white  object:  in  the  latter 
case  we  do  not  see  colored  borders. 

58.  Phenomena  of  Dispersion,  the  Pupil  Being  Partly  Covered.  —  It  is 

different  if  a  part  of  the  pupil  be  covered  by  a  screen.  Let  us  fix,  for  ex- 
ample, the  sash  bar  of  a  window  through  which  we  see  the  sky.  Cover- 
ing the  right  half  of  the  pupil  with  a  screen,  we  see  the  border  aa  (fig.  76) 
become  colored  blue,  the  border  bb  yellow.  In  order  to  explain  this  fact 
let  us  examine  the  point  a,  the  last  luminous  point  of  the  window  on  the 
right,  and  suppose  that  the  point  A  in  figure  75  is 
this  point:  by  covering  the  half  (BO,  fig.  75)  of  the 
pupil,  instead  of  a  circle  of  diffusion  uniformly  illum- 
inated by  violet  and  red,  we  have  a  circle  the  right  half 
of  which  is  violet  and  the  left  half  red.  This  latter  half 
is  covered  by  the  circle  of  diffusion  of  the  following 
point  of  the  window  on  the  right,  and  is  not  visible ; 
there  remains,  therefore,  a  blue  border  (violet)  along 
the  sash  bar.  Of  the  point  b  it  is,  on  the  contrary,  Fig.  76. 

the  red  half  (yellow)  of  the  circle  of  diffusion  which  is  not  covered.  — 
We  frequently  observe  very  striking  phenomena  due  to  the  chromatic 
aberration  of  the  eye,  by  fixing  black  objects  on  a  white  ground,  placed 
at  a  distance  for  which  the  eye  cannot  accommodate  itself.  Looked  at 
towards  the  sky,  the  slits  of  the  optometer  of  Young  present  thus  very 
vivid  colorings.  —  The  chromatic  aberration  increases  with  the  diameter 
of  the  pupil.  To  study  it,  it  is  useful,  therefore,  to  make  use  of 
mydriatics. 


114  PHYSIOLOGIC   OPTICS 

59.  Correction  of  the  Chromatic  Aberration.  —  We  could  correct  the 
chromatic  aberration  of  the  eye  with  a  concave  lens  of  Hint,  exactly  as  we 
can  correct  the  chromatic  aberration  of  a  convex  lens  of  crown  glass. 
The  dispersion  of  flint  glass  is  about  three  times  that  of  the  eye.  As 
the  refracting  system  of  the  eye  is  about  sixty  dioptrics,  a  concave  flint 
lens  of  about  twenty  dioptrics  would  be  necessary  to  correct  this  aberra- 
tion. A  myope  of  twenty  dioptrics,  who  would  correct  his  ametropia 
with  a  flint  lens,  would  have,  therefore,  at  the  same  time  corrected  his 
chromatic  aberration.  An  emmetrope  would  be  obliged  to  add  to  this 
lens  a  convex  achromatic  lens  of  twenty  dioptrics  to  remain  emmetropic. 
The  attempts  which  have  been  made  in  this  direction  (Helmholtz,  JavaT) 
have  not  given  a  very  marked  improvement  of  the  visual  acuity. 

Bibliography.  —  (Euvres  de  Young,  p.  154.  —  Wollaston,  Phil,  trans.,  1801,  p.  50.  — 
Fraunhofer(J.)  Gilberts  Ann.,  LVI, p.  304.  —  v.  Bezold  (W.).  Graefes  Arch.  f.  Ophth.,XlV 
2,  p.  1. 


CHAPTER  IX. 
REGULAR  ASTIGMATISM. 

60.  Optic  Principles.  Astigmatism  Produced  by  the  Form  of  the  Sur- 
faces. —  To  account  for  the  form  of  the  astigmatic  pencil,  the  following 
experiment  may  be  made.  We  combine  a  convex  cylinder,  with  its  axis 
horizontal,  with  a  convex  spherical  lens;  the  combination  of  +  3  cyl. 
with  4-  6  sph.  answers  very  well.  The  pencil,  which  emanates  from  a 


Ooi 


0  O 


Fig.  77.  —  Circles  of  diffusion  and  focal  lines  of  a  regularly  astigmatic  system.  After  Fuchs. 
(In  order  that  the  figure  may  agree  with  the  text,  we  must  suppose  the  first  focal 
line  a  horizontal,  the  second  6  vertical.) 

distant  luminous  point  and  is  refracted  by  the  sphero-cylindrical  com- 
bination, is  received  on  a  screen  which  is  gradually  moved  away  from 
the  lens.  Then,  instead  of  a  circle  of  diffusion,  the  diameter  of  which 
diminishes  according  as  the  screen  is  removed  in  order  to  become  a 
point  when  the  screen  is  at  focus,  and  to  again  become  circular  beyond, 
we  obtain  the  forms  illustrated  on  figure  77. 

The  two  straight  lines  are  called  focal  lines;  the  distance  which  sep- 
arates them  is  called  interfocal  distance,  and  the  meridians  of  the  optic 
system  to  which  they  correspond  are  the  principal  meridians.  Together 
the  rays  no  longer  form  a  cone  in  which  all  the  rays  pass  through  a 
point,  but  a  more  complicated  system,  characterized  by  this  peculiarity, 
that  all  the  rays  pass  through  two  short  straight  lines  perpendicular  to 
each  other  (the  focal  lines).  The  system  is  known  as  the  conoid  of 
Sturm. 

The  first  focal  line  is  at  the  focus  of  the  meridian  of  greatest  refrac- 
tion (in  our  case,  the  vertical  meridian) ;  it  is  parallel  to  the  meridian 

115 


116 


PHYSIOLOGIC  OPTICS 


of  least  refraction ;  the  second  focal  line  is  at  the  focus  of  the  meridian 
of  least  refraction  and  parallel  to  the  meridian  of  greatest  refraction. 
The  diffusion  spots  are  everywhere  elliptical,  except  at  one  point  of  the 
interfocal  distance  where  the  luminous  spot  is  circular. 

In  the  principal  meridians,  refraction  takes  place  as  if  the  lenses  were 
spherical ;  an  incident  ray  parallel  to  the  axis  cuts  the  latter  at  the  focus 
of  the  meridian.  The  rays  which  are  not  situated  in  the  principal  meri- 
dians do  not  meet  the  axis ;  their  course  will  be  indicated  later  on. 

The  length  of  the  focal  lines  is  proportional  to  the  distance  of  these  lines 
from  the  lens.  Let  F'  (fig.  78)  (i)  be  the  distance  of  the  first  focal  line, 


F; 


Fig.  78.  —  pu  horizontal  focal  line ;  p.2,  vertical  focal  line. 

F"  that  of  the  second,  P  the  diameter  of  the  lens,  p±  and  p2  the  lengths 
of  the  two  focal  lines.    Then  we  have 


PI 
~" 


—  F' 


and 


^—   —  ;  consequently  by  dividing 


The  circle  of  circular  diffusion  is  at  a,  where  the  diameters  are  equal. 
It  divides  the  interfocal  distance  into  two  parts,  which  are  proportional  to 
the  focal  distances.  For,  designating  the  diameter  at  this  place  by  a,  and 
the  two  parts  of  the  interfocal  distance  by  x  and  y  we  have  : 


and  - 


,  therefore,  by  dividing, 


y     .  PL  - 

x      ~  Pl   ~  -  F' 


All  the  other  diffusion  spots  are  ellipses,  of  which  it  is  easy  to  calculate 


(1)  We  must  suppose  that  the  vertical  meridian  has  been  made  to  rotate  90°  around  the  axis,  so  as  to 
be  able  to  draw  the  two  focal  lines  in  the  same  plane. 


REGULAR  ASTIGMATISM 


117 


the  axes.  Placing  a  screen  at  a  distance  b  from  the  second  focal  line, 
we  see  (fig.  78)  that  the  axes  c  and  d  of  the  ellipse  are  found  by  the 
equations  -£-  =  l  ~  (Ff,  ~  F°  and  -|-  =  •£- ,  equations  which  give  as  the 
relation  between  the  axes: 


—  (F"  —  FQ 
~F/~~ 


X 


Knowing  the  axes  we  can  find  the  ellipse  by  construction  (fig.  79). 
We  make  a  circle  with  half  the  long  axis  d  (fig.  78)  as  radius,  and  draw 
therein  two  diameters,  a  horizontal  BD  and  a  vertical  AE,  and  mark 
the  points  A'  and  E'  so  that  OA'  =  OE'  =  -f .  BD  and  A'E'  are  then 


Fig.  79.  —  Construction  of  the  elliptical  diffusion  spot. 

the  two  axes  of  the  ellipse,  and  we  can  find  any  point  whatever  Gx,  of 
the  ellipse,  by  letting  fall  the  perpendicular  GH  on  the  long  axis,  and 
marking  the  point  G^  so  that  %g-  =  -£- . 

We  can  use  this  construction  to  find  the  course  of  the  rays  which 
are  not  situated  in  the  principal  planes.  Suppose,  indeed,  that  one  of 
these  rays  passes  through  a  given  point  of  the  lens.  If  the  optic  system 
were  spherical  and  of  the  power  of  the  meridian  of  least  refraction,  we 
would  have  a  circle  of  diffusion  of  diameter  BD,  in  which  it  would  be 
easy  to  find  the  point  K  through  which  the  ray  would  pass,  since  the 
circle  would  be  only  a  diminished  image  of  the  lens.  Having  determined 
the  position  of  the  point  K,  we  find  the  point  K'  through  which  the 
ray  really  passes,  by  diminishing  the  distance  of  K  from  the  long  axis 
in  the  proportion  -|-. 

APPLICATION  OF  THE  PRINCIPLE  OF  FOUCAULT.  —  Let  us  place  the 
luminous  point  a  little  beyond  the  focus  of  our  sphero-cylindrical  com- 


118  PHYSIOLOGIC  OPTICS 

bination.  The  focal  lines  are  then  formed  at  quite  a  great  distance.  We 
receive  the  horizontal  focal  line  on  a  screen  which  is  then  removed  and 
the  eye  put  in  its  place ;  we  will  then  see  a  vertical  luminous  band  which 
passes  through  the  lens,  while  the  parts  on  the  right  and  left  are  dark. 
As  we  have  already  seen  (page  99)  the  eye  sees  luminous  the  parts  of 
the  lens  which  send  light  to  it,  and  it  is  easy  to  see  that  it  receives  under 
these  circumstances  all  the  luminous  rays  from  the  vertical  meridian, 
while  it  does  not  receive  rays  coming  from  the  lateral  parts  which  inter- 
sect in  other  points  of  the  horizontal  focal  line,  to  the  right  and  left 
of  the  eye.  Placing  the  eye  in  the  vertical  focal  line  we  see  a  horizontal 
band. 

61.  Defects  of  the  Image.  —  As  the  image  of  a  point  is  never  exactly 
a  point,  the  image  of  an  object  can  never  be  really  distinct.  Outside  the 
focal  lines,  the  outlines  are  all  more  or  less  dull.  If  the  screen  is  at  plt 
the  horizontal  lines  only  are  distinct,  if  it  is  at  p2,  it  is  the  vertical  lines 
that  are  distinct.  The  image  is  better  at  p±  than  at  p2,  since  the  first 
focal  line  is  the  shorter. 

With  a  cylinder  which  is  strong  compared  with  the  spherical  glass, 
the  image  becomes  so  poor  that  it  is  unrecognizable ;  with  +  6  spherical 
combined  with  +  3  cylindrical  of  our  test  case,  it  is  impossible  to  form 
an  image  on  a  screen.  If,  on  the  contrary,  we  place  this  combination 
sufficiently  far  from  the  eye  that  the  image  may  be  seen  inverted,  this 
image  is  pretty  good,  because  the  pupil  of  the  observer  forms  a  dia- 
phragm ;  but  it  is  deformed,  all  the  dimensions  parallel  to  the  meridian 
of  greatest  refraction  being  greatly  diminished. 

€2.  Astigmatic  Surfaces.  —  We  have  so  far  obtained  astigmatic  refrac- 
tion by  a  combination  of  spherical  and  cylindrical  surfaces,  but  we  can 
obtain  the  same  result  by  refraction  through  a  single  refracting  sur- 
face. —  If  the  aperture  is  very  small,  this  result  is  obtained  with  any 
surface  whatever,  (i)  For,  a  small  part  of  any  surface  always  presents 
two  principal  meridians,  perpendicular  to  each  other,  one  of  maximum 
and  the  other  of  minimum  curvature.  The  incident  rays,  situated  in 
these  planes,  remain  there  after  refraction  and  go  to  meet  the  axis  after 
refraction;  the  rays  which  are  not  situated  in  these  meridians  do  not 
meet  the  axis,  but  pass  through  two  focal  lines,  perpendicular  to  the 
axis  and  situated  in  the  principal  meridians.  —  Among  the  surfaces  for 
which  this  is  true,  even  for  quite  a  large  aperture,  at  least  approximately, 

(1)  We  must  except  the  plane,  sphere,  the  part  near  the  axes  of  the  surfaces  of  revolution,  and  that 
near  the  points  called  umbilical  of  other  surfaces,  supposing  the  incidence  normal.  Otherwise,  the  re- 
fraction is  always  astigmatic. 


REGULAR  ASTIGMATISM  119 

there  are  two  specially  noteworthy:  the  ellipsoid  with  three  axes  and 
the  tore. 

By  rotating  an  ellipse  around  its  long  axis,  we  obtain  an  ellipsoid  of 
revolution.  And  if  we  suppose  that  it  undergoes  a  flattening  in  a  direc- 
tion perpendicular  to  the  long  axis,  we  obtain  an  ellipsoid  with  three  axes. 
The  luminous  point  must  be  on  the  long  axis.  —  The  two  principal 
meridians  are  elliptical  (as  is  every  other  section  of  this  surface). 

The  tore  is  the  surface  which  is  obtained  by  making  a  circle  rotate 
around  an  axis  situated  in  its  plane  (ab,  fig.  80).  By  cutting  a  part  near 
A,  we  would  have  an  astigmatic  surface  the  principal  meridians  of  which 
would  be  circular ;  one  would  have  the  same  radius  as  the  circle  (Rt) ; 
the  radius  of  the  other  (R2)  would  be  equal  to  the  distance  of  the  axis 
from  the  apex  of  the  circle.  The  luminous  point  must  be  on  the  pro- 
longation of  AO. 

Even  with  these  surfaces  a  pure  astigmatic  action  is  not  obtained, 
when  the  aperture  is  a  little  large.  It  is 
clear  that  on  account  of  the  spherical 
aberration  the  peripheral  parts  of  the 
principal  meridians  of  the  tore  must  have 
a  greater  refraction  than  the  central 
parts ;  also  the  astigmatism  of  a  periph- 
eral zone  becomes  greater  than  that 
of  the  central  part,  since  the  refraction 
increases  more  rapidly  towards  the  pe- 
riphery in  the  most  curved  principal  me- 
ridian. —  On  account  of  the  flattening 

towards  the  periphery,  the  aberration  is     Fig-  80-  ~  »7  the  revolution  around 

the  straight  line  06,  the  circle  pro- 

less  for  the  ellipsoid ;  one  of  the  men-       duces  a  torus, 
dians  may  even  be  aplanatic  for  a  distant  object,  but  then  the  other  meri- 
dian is  either  over-corrected  or  under-corrected,  so  that  the  astigmatic 
effect  is  never  pure. 

63.  Astigmatism  by  Incidence.  —  Let  us  place  a  spherical  lens  at  some 
distance  from  a  luminous  point  and  form  the  image  of  this  point  on  a 
screen;  then  make  the  lens  rotate  around  a  vertical  axis.  The  screen 
immediately  ceases  to  be  at  the  point ;  we  must  move  it  nearer  the  lens, 
and  we  find  at  the  same  time  that  the  refracted  pencil  is  astigmatic.  The 
horizontal  focal  line  is  farther  from  the  lens  than  the  vertical  focal  line. 
The  refraction  has,  therefore,  increased  in  both  meridians,  but  more  in  that 
which  contains  the  axis  of  the  lens  and  the  luminous  point. 


120 


PHYSIOLOGIC  OPTICS 


The  focal  lines  are  far  from  being  distinct,  especially  if  we  do  not 
use  a  small  diaphragm.  They  are  rather  diffusion  spots  greatly  length- 
ened in  one  or  other  direction.  —  But  the  pencil  has  one  true  focal  line 


Fig.  81.  —  Focal  line  of  a  lens  placed  obliquely. 

which,  in  our  case,  is  horizontal ;  we  find  it  by  making  the  screen  rotate 
around  a  vertical  axis,  but  in  a  direction  the  reverse  of  that  of  the  lens 

(fig.  81). 

A  pencil  reflected  or  refracted  obliquely  by  a  spherical  surface  is  also 
astigmatic  by  incidence.  It  is  the  same  phenomenon  which  constitutes 
spherical  aberration. 

Let  cabd  (fig.  82)  be  an  incident  pencil  parallel  to  the  axis  of  a  refract- 
ing spherical  surface.  Suppose  that  the  pencil  is  cylindrical,  so  that  ab 


Fig.  82. 
Astigmatism  by  incidence.  —  Fx,  first  focal  line  ;  Fx/  F//x,  second  focal  line. 

is  the  diameter  of  the  small  round  spot  which  represents  the  aperture 
of  the  surface :  ab  is  then  one  of  the  principal  meridians  and  the  diameter 
perpendicular  to  ab  is  the  other.  On  account  of  the  spherical  aberra- 
tion the  ray  aF'  meets  the  axis  nearer  the  surface  than  the  ray  bFr.  The 
first  focal  line,  which  is  perpendicular  to  the  plane  of  the  paper,  is  at  F', 
for,  if  we  imagine  the  entire  figure  rotating  around  the  axis,  F'  describes 
an  arc  of  a  circle,  a  small  part  of  which  may  be  considered  as  a  straight 


REGULAR  ASTIGMATISM  121 

line,  and  it  is  easy  to  see  that  all  the  rays  of  our  pencil  must  pass  through 
this  straight  line  (at  least  approximately).  As,  on  the  other  hand,  the 
rays  must  all  meet  the  axis,  F"  F"'  is  the  second  focal  line.  —  Here 
again  the  meridian  of  greatest  refraction  is  that  which  contains  the  axis. 

When  the  incidence  is  oblique,  all  the  surfaces,  the  plane  surfaces  in- 
cluded, give  astigmatism  by  refraction. 

It  is  the  same  in  the  case  of  reflection,  but  then  the  plane  surfaces 
are  an  exception.  Ordinary  mirrors  are  not  exempt  from  this  defect 
on  account  of  the  refraction  through  the  thickness  of  the  glass  which 
is  in  front  of  the  coating.  The  best  images  that  we  can  obtain  are  those 
formed  by  reflection  on  a  surface  of  mercury,  especially  when  the  layer 
is  very  thin:  the  pencil  is  not  astigmatic  at  all.  (i) 

64.  Astigmatism  of  the  Human  Eye.  Historical.  —  This  defect  of  the 
human  eye  was  discovered  by  Thomas  Young  in  1801.  He  never  noticed 
that  his  vision  was  defective,  and  claimed  that  he  saw  as  well  as  most 
people.  He  proved  the  defect  in  his  own  eye  by  means  of  his  optometer, 
and  also  by  observing  the  forms  of  the  circles  of  diffusion  produced  by 
a  luminous  point.  He  measured  its  degree  by  means  of  the  optometer 
and  expressed  it,  as  we  still  do,  by  the  difference  of  refraction  of  the  two 
meridians.  He  had  1.7  D.  of  astigmatism  against  the  rule.  He  proved 
that  his  astigmatism  was  not  seated  in  the  cornea,  because,  by  perform- 
ing his  celebrated  experiment  of  putting  the  eye  under  water  and  sub- 
stituting a  spherical  lens  for  the  cornea  (see  page  168),  he  found  the 
same  degree.  —  He  attributed  the  astigmatism  to  the  obliquity  of  the 
crystalline  lens,  which  obliquity  he  thought  much  greater  than  it  really 
is,  and  remarked  that  the  defect  could  be  corrected  with  glasses  placed 
obliquely  in  front  of  the  eye. 

The  astronomer  Airy,  a  professor  at  Cambridge,  was  the  first  who 
corrected  the  defect  by  a  cylindrical  glass  (1827).  He  had  high  com- 
pound myopic  astigmatism  of  the  left  eye,  which  he  studied  and  meas- 
ured by  means  of  a  luminous  point.  —  Later,  Colonel  Goulier  likewise 
studied  this  defect  and  prescribed  cylindrical  glasses  to  a  certain  number 
of  patients. 

It  was  only  after  the  invention  of  the  ophthalmometer  by  Hclmlwltz 
that  the  measurements  of  Knapp  and  Bonders  drew  attention  to  this 
prevalent  anomaly  of  the  human  eye.  The  works  of  these  two  investi- 
gators appeared  almost  at  the  same  time,  but  those  of  Bonders  had 


(1)  It  is  claimed,  however,  that  we  can  still  observe  a  trace  of  astigmatism,  in  this  case,  -with  the 
telescopes  of  the  greatest  magnifying  power.  This  astigmatism  might  be  due  to  the  fact  that  the  sur- 
face is  not  really  plane  on  account  of  the  spherical  form  of  the  earth. 


122  PHYSIOLOGIC   OPTICS 

greater  influence.  He  was,  in  fact,  the  first  to  have  cylindrical  glasses 
put  in  the  test  case,  which  greatly  contributed  to  their  more  general 
use.  The  methods  used  for  the  examination  of  patients  were  quite  de- 
fective. The  luminous  point  was  especially  used  to  find  the  meridians, 
and  the  refraction  of  each  meridian  was  then  measured  by  means  of  the 
stenopaic  slit  and  spherical  glasses.  —  A  little  later  Javal  introduced 
the  examination  by  the  star  figure  and  cylindrical  glasses. 

65.  Physiologic  Astigmatism.  —  It  is  rare  to  find  an  eye  completely 
free  from  astigmatism ;  but  when  the  degree  is  slight,  it  scarcely  affects 
the  vision.    We  call  this  astigmatism  physiologic.    It  is  a  disputed  ques- 
tion at  what  degree  we  should  begin  to  consider  astigmatism  pathologic ; 
some  have  placed  the  limit  at  0.5  D.  or  at  0.75  D.,  others  at  I  D.  or 
1.5  D.    In  certain  people  we  can  improve  vision  with  a  cylinder  of  0.75 ; 
others,  on  the  contrary,  experience  no  improvement,  although  they 
may  have  really  the  same  degree  of  astigmatism.    The  aperture  of  the 
pupil,  and  especially  the  greater  or  less  regularity  of  the  astigmatic 
pencil,  here  play  an  important  part.    One  of  the  best  means  of  disclosing 
low  degrees  of  astigmatism  consists  in  observing  the  form  under  which 
a  luminous  point  appears  when  placed  at  different  distances.     If  the 
luminous  point  indicates  a  trace  of  astigmatism,  we  can  generally  also 
verify  'it  by  the  star  figure  and  a  weak  cylindrical  lens,  by  placing  the 
latter  at  first  in  the  correct  position  and  then  in  the  contrary  position. 
The  patient  then  tells  that  the  former  position  equalizes  the  lines  better 
than  the  latter. 

66.  Corneal  Astigmatism.  —  The  principal  seat  of  astigmatism  is  in 
the  anterior  surface  of  the  cornea,  which  is  not  strange,  since  it  is  at  this 
place  that  the  principal  change  of  index  occurs.    A  deformity  of  one  of 
the  internal  surfaces  of  the  eye,  which,  at  the  anterior  surface  of  the 
cornea,  would  produce  considerable  astigmatism,  has  only  slight  effect 
on  account  of  the  little  difference  of  index  of  the  media.    The  refraction 
is  expressed,  as  we  have  seen,  by   (n  ~£ 10  '    (see  page   13),  that  is  to 
say,  for  the  cornea,  by  -™  and,  for  one  of  the  internal  surface,  by 
~.     The  same  deformity  would,  therefore,  produce  an  effect  five  or 
six  times  less. 

We  may  conceive  also  that,  in  the  normal  eye,  astigmatism  by  in- 
cidence could  scarcely  play  any  part,  since  the  visual  line  passes  ap- 
proximately through  the  center  of  curvature  of  the  cornea  and  through 
the  middle  of  the  pupil.  It  is  otherwise  in  cases  where  there  exists  a 
considerable  displacement  of  the  pupil  (corectopia),  and  especially  in 


REGULAR  ASTIGMATISM 


123 


the  case  of  an  artificial  pupil.  —  Under  ordinary  circumstances,  there- 
fore, it  is  the  form  of  the  anterior  surface  of  the  cornea  that  principally 
determines  astigmatism;  the  examination  of  this  surface  thus  plays  an 
important  part  in  the  search  for  astigmatism. 

67.  Measurement  of  Corneal  Astigmatism.  —  There  exist  different 
means  of  examining  whether  the  cornea  is  astigmatic  and  of  estimating 
the  degree  of  its  deformity  (disc  of  Placido,  keratoscope  of  de  Wecker 
and  Massclon,  etc.) ;  but,  to  measure  it,  one  can  scarcely  think  of  using 
any  other  means  than  the  ophthalmometer  of  Javal  and  Schioetz,  which 
we  have  already  described.  The  progress  which  it  marks,  compared 
with  old  ophthalmometers,  consists  especially  in  the  facility  with  which 
we  find  the  principal  meridians  by  means  of  the  difference  in  the  level 
(denivellatiori).  If  the  arc  is  in  a  principal  meridian,  the  images  of  the 
two  mires  must  be  on  the  same  level  and  the  black  lines  which  are  at 
the  middle  of  the  mires  must  be  in  the  prolongation  of  each  other.  Out- 
side the  principal  meridians  there  is  a  difference  in  the  level  (denivellatiori) 
greater  in  proportion  as  the  astigmatism  is  more  pronounced. 


Fig.  83.  —  Explanation  of  the  difference  in  the  level  (de"nivellation). 

To  explain  this  phenomenon,  let  us  examine  a  spherical  cornea  after 
having  removed  the  doubly  refracting  prism  from  the  instrument  which 


124  PHYSIOLOGIC  OPTICS 

then  acts  as  a  simple  telescope.  We  then  see  only  the  images  of  the 
two  mires,  separated  by  an  interval  of  about  3  millimeters.  By  rotating 
the  arc  these  images  describe  a  circle.  Let  ABCD,  figure  83,  be  this 
circle  to  which  the  images  of  the  mires  always  remain  tangents.  Let 
us  replace  the  prism  in  position.  Then  the  images  are  in  the  same 
meridian  as  the  mires  themselves,  and  as  the  doubling  (dedoublemcnt)  of 
the  prism  takes  place  exactly  in  this  meridian  there  is  no  difference  in 
the  level.  —  If  we  replace  the  spherical  cornea  by  an  astigmatic  cornea, 
the  vertical  meridian  of  which  is  the  more  curved,  the  circle  ABCD  is 
replaced  by  the  ellipse  AEBF  which  is  constructed  as  shown  on  page  117 
by  reducing  the  distance  of  each  point  from  AB  in  the  proportion  of 
the  radii  of  the  two  principal  meridians.  By  this  construction  the  dotted 
diameter  becomes  the  diameter  KL,  on  which  the  images  now  are.  The 
latter  are,  therefore,  no  longer  situated  in  the  meridian  of  the  mires, 
and  as  the  prism  always  acts  in  the  direction  parallel  to  this  meridian,  it 
follows  that  on  obtaining  contact  the  two  images  are  not  on  the  same 
level.  Only  when  the  arc  is  in  one  of  the  principal  meridians  the  mires 
and  their  images  are  in  the  same  plane  and  there  is  no  difference  in 
the  level. 

We  can  account  for  the  difference  between  the  image  produced  by  a 
spherical  cornea  and  that  of  an  astigmatic  cornea,  by  drawing  on  a  sheet 
of  paper  a  circle  with  two  oblique  diameters,  perpendicular  to  each 
other,  and  observing  the  inverted  image  formed  by  a  strong  spherical 
lens  held  at  some  distance  from  the  eye.  The  image  is  identical  with 
the  drawing;  but  if  a  convex  cylinder  with  horizontal  axis  be  added, 
the  circle  is  replaced  by  an  ellipse  with  the  long  axis  horizontal,  and  the 
two  diameters  form  between  them  obtuse  angles  above  and  below. 

After  having  placed  the  ocular  in  focus  for  the  spider  thread,  and 
then  the  instrument  in  focus  for  the  eye,  we  begin  by  finding  the  meri- 
dian of  least  refraction.  We  place  the  mires  in  contact  and  make  the 
arc  rotate  90°.  This  done,  the  images  of  the  mires  partly  overlap,  and 
the  number  of  gradations  overlapped  indicates  the  degree  of  astig- 
matism in  dioptrics.  —  If  very  exact  measurements  are  desired,  it  is 
preferable  to  find  each  of  the  meridians  separately,  and  to  obtain  contact 
in  each  of  them.  We  read  the  refraction  of  each  meridian  on  the  arc, 
and  the  difference  indicates  the  astigmatism.  —  We  sometimes  observe 
that  the  two  principal  meridians  are  not  exactly  perpendicular  to  each 
other;  this  is  due  to  the  relatively  great  distance  between  the  mires; 
for,  the  principal  meridians  of  a  minute  part  of  a  surface  are  always 
perpendicular  to  each  other.  —  This  is  attributable  to  the  fact  that  the 


REGULAR  ASTIGMATISM  125 

meridians,  instead  of  being  plane  sections  of  the  cornea,  possess  a 
certain  curvature. 

68.  Regular  Corneal  Astigmatism.  —  We  distinguish  between  direct 
astigmatism  or  astigmatism  with  the  rule,  in  which  the  meridian  of 
greatest  refraction  does  not  differ  much  from  the  vertical,  and  perverse 
astigmatism  or  astigmatism  against  the  rule,  in  which  the  horizontal 
meridian  is  that  of  greatest  refraction.    If  the  direction  of  the  meridians 
differs  much  from  the  horizontal  and  vertical  directions,  we  say  that 
the  astigmatism  is  oblique. 

Schioets  and  Nordenson  have  compiled  statistics  on  the  direction  of  the 
corneal  astigmatism  in  school  children.  Following  are  the  results  ob- 
tained by  Nordenson: 

Corneal  astigmatism,  none 9  per  cent. 

with  the  rule 77       — 

against  the  rule 1       — 

oblique 12       — 

Thirty  per  cent,  had  astigmatism  of  at  least  I  D.,  2  per  cent,  an  astig- 
matism over  1.5  D.  —  It  seems  that  astigmatism  against  the  rule  be- 
comes more  frequent  with  age,  and  that  astigmatism  with  the  rule 
changes  into  astigmatism  against  the  rule  under  the  influence  of  an 
increase  of  tension.  Pfalz  and  G.  Martin  have  thus  found  astigmatism 
against  the  rule  very  common  in  glaucomatous  patients,  and  the  ex- 
perimental researches  of  Eissen  on  rabbits'  eyes  confirm  this  result. 

Except  in  post-operative  cases,  corneal  astigmatism  only  very  rarely 
exceeds  the  degree  of  5  to  6  D. ;  astigmatism  against  the  rule  and  oblique 
astigmatism  are  never  so  pronounced.  —  If  there  is  a  difference  between 
the  degree  of  the  astigmatism  of  the  two  eyes  of  the  same  person,  we 
generally  find  that  the  most  astigmatic  eye  has  the  maximum  curvature 
greater  and  the  minimum  curvature  less  than  those  of  the  other  eye, 
but  the  difference  is  generally  greater  for  the  meridian  of  greatest  refrac- 
tion (Javal). 

69.  Relations  Between  Ophthalmometric  and  Subjective  Astigmatism.  — 
We  have  said  that  the  first  ophthalmometric  measurements  were  made 
by  Bonders  and  Knapp.    They  noticed  that  there  existed  a  certain  differ- 
ence between  the  ophthalmometric  and  subjective  measurements.  They 
attributed  this  difference  to  an  astigmatism  of  the  crystalline  lens  which 
would  act  in  a  direction  contrary  to  that  of  the  cornea.     Since  then 
much  has  been  said  of  crystalline  astigmatism,  but  what  has  been  said 


126  PHYSIOLOGIC  OPTICS 

about  it  is  purely  hypothetical,  for  if  I  except  some  measurements  which 
I  have  made  with  the  ophthalmophakometer,  and  to  which  I  shall  refer 
later,  I  do  not  think  that  any  one  has  observed  directly  astigmatism  of 
the  crystalline  lens.  Now,  the  difference  between  ophthalmometric  and 
subjective  astigmatism  may  be  attributed  to  many  other  causes.  To 
assume  nothing  as  to  the  nature  of  this  astigmatism  I  shall  call  it  supple- 
mentary astigmatism.  According  to  most  investigators  the  part  which 
it  plays  is  the  following: 

i°  If  there  is  no  ophthalmometric  astigmatism,  we  generally  find  a 
slight  subjective  astigmatism  against  the  rule; 

2°  If  the  ophthalmometric  astigmatism  is  against  the  rule,  the  sub- 
jective astigmatism  is  generally  against  the  rule  and  greater; 

3°  If  the  ophthalmometric  astigmatism  is  with  the  rule  and  of  a  value 
intermediate  between  I  and  3  D.,  the  subjective  astigmatism  generally 
differs  only  slightly  from  it; 

4°  If  the  ophthalmometer  gives  an  astigmatism  with  the  rule  and 
greater  than  3  D.,  the  subjective  astigmatism  is  also  with  the  rule,  fre- 
quently greater. 

Javal  tried  to  express  the  relation  between  subjective  astigmatism 
(Ast)  and  ophthalmometric  astigmatism  (Asc)  by  the  empiric  formula: 

Ast  =  k  +  p.  A»c, 

in  which  formula  k  and  p  are  two  constants,  k  =  0.5  D.  against  the  rule 
and  p  =  1.25.  —  This  formula  would  give  the  following  relation: 

Against  the  rule.  With  the  rule. 

As.  opht.    2  —     1      —    0    —     1—2—      3—4-        5     —  6  dioptrics 
As.  sub).     3  —  1.75  —  0.5  —  0.75  —  2  —  3.25  —  4.5  —  5.75  —  7  dioptries 

Against  the  rule.  With  the  rule. 

It  is  well  understood  that  this  permits  of  many  exceptions,  for  supple- 
mentary astigmatism  depends  on  so  many  factors,  that  it  is  very  difficult 
to  give  a  general  expression  of  its  value.  Among  these  factors  I  shall 
state  the  following: 

i°  The  Deformity  of  the  Internal  Surfaces.  —  Although  these  deform- 
ities, as  I  have  already  remarked,  play  quite  an  important  part  in  the 
literature,  this  question  has,  up  to  the  present,  been  completely  ignored. 
To  give  an  idea  of  the  part  which  they  might  play,  I  add  the  following 
table,  which  gives  the  results  for  some  eyes  I  have  measured : 


REGULAR  ASTIGMATISM  127 

Mme  T.  Dr.  B.  M.  V. 

Thickness  of  the  cornea I.l5mm  1.06mm  1.31mm 

Position  of  the  anterior  surface  of  the  crystalline        3.54mm  4.24mm  3  66mm 

Thickness  of  the  crystalline - 4.06mm  3.98mm  4.25ram 

Anterior  surface  of  the  cornea : 

Kadius.     Horizontal  meridian 7.98mm  7.78mm  8  29mm 

Vertical  meridian 7.60mm  7.90mm  8.33mm 

Horizontal  refraction 47.24  D.  48.46  D.  45.48  D. 

Vertical  refraction  49.60  D.  47.72  D.  45.26  D. 

Posterior  surface  of  the  cornea  : 

Radius.    Horizontal  meridian 6.22mm        5.66mm        6.17min 

Vertical  meridian 5.55mm        5.11jnm        5.87mni 

Horizontal  refraction —  4.73  D.  —  5.19  D.  —  4.77  D. 

Vertical  refraction —  5.30  D.  —  6.76  D.  —  5.01  D. 

Anterior  surface  of  the  crystalline  lens: 

Radius.     Horizontal  meridian 10.20mni  12.26mm  10.42mn» 

Vertical  meridian  10.10mm  10.09mm  9.33mm 

Horizontal  refraction 6.13  D.  5.10  D.  6.00  D. 

Vertical  refraction 6.19  D.  6.19  D.  6.70  D. 

Posterior  surface  of  the  crystalline  lens: 

Radius.     Horizontal  meridian  6.17mm  6.38mm  6.73mm 

Vertical  meridian 6.24mm  7.11mm  8.49mm 

Horizontal  refraction 9.63  D.  9.22  D.  8.73  D. 

Vertical  refraction 9.42  D.  8.27  D.  6.93  D. 

Astigmatism  in  Dioptrics :  (1) 

Anterior  surface  of  the  cornea 2.36  d  0.74  i  0.22  i 

Poterior  surface  of  the  cornea 0.57  i  0.57  i  0.24  i 

Anterior  surface  of  the  crystalline  lens 0.06  d  1.09  d  0.70  d 

Posterior  surface  of  the  crystalline  lens 0.11  i  0.95  i  1.81  i 

Complete  system 1.40  d  1.05  i  1.62  i 

Although  we  manifestly  cannot  draw  general  conclusions  from  the 
measurements  of  three  eyes,  I  wish,  however,  to  direct  attention  to  some 
of  these  results.  We  observe  in  the  first  place  that  the  vertical  meri- 
dian of  the  posterior  surface  of  the  cornea  presents  a  more  pronounced 
curvature  than  the  horizontal  meridian.  This  condition  is  repeated  in 
the  three  eyes  to  which  I  here  refer,  as  well  for  the  first,  the  anterior  sur- 
face of  which  presents  astigmatism  with  the  rule,  as  for  the  other  two 
in  which  it  presents  astigmatism  against  the  rule.  I  have  also  met  the 
same  deformity  in  other  eyes  which  I  have  measured,  so  much  so  that 
there  is  reason  to  believe  that  the  condition  is  general.  It  is  a  deformity 
analogous  to  that  which,  in  the  case  of  the  anterior  surface  of  the 
cornea,  produces  astigmatism  with  the  rule;  but,  as  the  posterior  sur- 
face acts  like  a  concave  lens,  this  deformity  produces  astigmatism  against 

(1)  [Here  d  (direct)  stands  for  astigmatism  with  the  rule  and  i  (indirect)  for  that  against  the 
rule.]— IF. 


128  PHYSIOLOGIC   OPTICS 

the  rule.  It  is  probably  for  this  reason  that  eyes,  which  have  no  ophthal- 
mometric  astigmatism,  generally  have  subjective  astigmatism  against 
the  rule.  The  influence  of  the  posterior  surface  of  the  cornea  must 
correspond  partly  with  the  term  k  of  the  formula  of  Javal. 

As  to  the  crystalline  surfaces,  we  observe  that  the  anterior  surface 
presents  in  the  three  cases  astigmatism  with  the  rule,  the  posterior 
surface  astigmatism  against  the  rule.  I  do  not  know  whether  it  is  a 
coincidence  or  whether  it  indicates  a  general  rule. 

2°  The  obliquity  of  the  crystalline  lens  must,  after  what  we  have  said  on 
refraction  by  lenses  placed  obliquely  (page  119),  produce  astigmatism 
against  the  rule,  but  very  little,  at  most  a  half  dioptry,  and  perhaps 
less,  if  the  special  structure  of  the  crystalline  lens  results  in  compensat- 
ing the  effect  of  its  obliquity  as  certain  authors  (Hermann)  have  sup- 
posed. 

3°  Mention  has  been  made  of  an  astigmatic  accommodation  of  the  crystal- 
line lens,  which  would  have  the  effect  of  correcting  the  corneal  deformity, 
and  often  even  over-correcting  it.  In  my  opinion  this  astigmatic  accom- 
modation is  not  sufficiently  demonstrated ;  I  shall  speak  of  it  forthwith. 

4°  We  must  not  forget  the  influence  of  the  distance  of  the  correcting  glass 
from  the  eye,  in  consequence  of  which  the  concave  correcting  glass  is 
stronger,  the  convex  glass  weaker  than  the  true  astigmatism.  This 
influence  makes  itself  felt  the  more  according  as  the  glass  is  stronger, 
and,  in  order  to  calculate  it,  we  must  take  into  account  not  only  the 
cylindrical  glass,  but  also  the  spherical  glass  with  which  it  is  combined 
(Ostwalt)  (i). — If  certain  authors  have  found  that  the  subjective  astigma- 
tism with  the  rule  frequently  exceeds  that  found  with  the  ophthalmo- 
meter  (the  factor  p  of  Javal),  it  is  due,  perhaps,  to  the  fact  that  they 
generally  use  concave  cylinders. 

5°  Among  the  factors  which  play  a  part  in  supplementary  astigma- 
tism, the  most  important  is  probably  the  variation  of  the  astigmatism 
in  the  different  zones  of  the  cornea.  The  peripheral  zones  frequently  pre- 
sent a  value,  and  sometimes  also  a  direction  more  or  less  different  from 
those  of  the  central  zones.  This,  among  other  things,  follows  from  the 
measurements  of  the  peripheral  parts  of  the  cornea  made  by  Sulzer; 
but  it  is  especially  after  I  began  to  work  with  the  optometer  of  Young 
that  I  frequently  found  considerable  differences  between  the  refraction 
of  different  parts  of  the  pupillary  space,  and  that  I  became  convinced 
of  the  importance  of  these  differences.  There  certainly  exist  some 
regularly  constructed  eyes,  in  which  the  astigmatism  is  nearly  the  same 

(1)  [See  also  an  article  by  the  translator  in  the  Archives  oj  Ophthalmology,  Vol.  XXII,  No.  1,  1893 
where  this  question  is  discussed  fully.]— IF. 


REGULAR  ASTIGMATISM  129 

in  the  whole  pupillary  space,  but  most  eyes  are  more  or  less  irregular. 
Entirely  regular  astigmatism  is  only  imaginary.  —  This  explains  also 
the  hesitancy  of  many  patients  when  tested  with  different  cylindrical 
glasses.  We  have  all  met  cases  in  which  it  is  almost  impossible  to 
obtain  a  definite  answer  from  the  patient.  Sometimes  he  prefers  one 
cylinder,  sometimes  another  somewhat  different,  and,  at  each  new  exam- 
ination, he  manifests  a  different  preference.  Most  frequently  if  the 
patient  hesitates,  he  has  good  reasons  for  doing  so.  —  Examination  with 
the  luminous  point  (see  chap.  X),  which  has  been  much  neglected,  but 
which  we  have  us"ed  for  some  time  at  the  laboratory  of  Soirbonne,  shows 
why  the  patient  hesitates  and  why  we  frequently  do  not  obtain  a  very 
encouraging  result  by  correction. 

70.  Astigmatic  Accommodation.  —  The  question  of  astigmatic  accom- 
modation has  been  much  discussed  for  some  years  past.  It  was  Dobro- 
wolsky  who  first  expressed  the  idea  that  astigmatic  patients  could  partly 
correct  their  defect  by  producing  a  deformity  of  the  crystalline  lens  in 
a  contrary  direction,  by  an  irregular  contraction  of  the  ciliary  muscle. 
He  thus  supposed  a  latent  astigmatism  which  could  be  made  manifest  by 
instilling  atropine,  exactly  as  in  the  case  of  hypermetropia.  —  Later,  the 
idea  was  adopted  by  Javal,  and  pushed  to  its  extreme  conclusions  by 
G.  Martin,  Vacher  and  others,  who  went  so  far  as  to  find  in  this  astig- 
matic accommodation  the  origin  of  a  series  of  diseases:  blepharitis, 
keratitis,  migraine  and  even,  in  certain  cases,  cataract.  Some  time  ago 
a  reaction  set  in ;  most  of  the  authors  in  later  years,  like  Eriksen,  Sulzer 
and  especially  George  Bull,  do  not  admit  astigmatic  accommodation. 

The  advocates  of  astigmatic  accommodation  based  their  belief  espe- 
cially on  the  change  of  the  astigmatism  observed  on  instilling  atropine. 
The  phenomenon  is,  in  all  probability,  due  to  the  fact  that  the  astig- 
matism of  the  peripheral  parts  differs  from  that  of  the  central  part;  in 
ordinary  circumstances  these  parts  are  outside  the  pupil,  but  in  con- 
sequence of  atropinization  the  latter  is  dilated  so  as  to  allow  the  pe- 
ripheral parts  to  come  into  play.  The  area  of  these  peripheral  parts  is 
generally  greater  than  that  of  the  central  part  which  corresponds  to 
the  pupil  in  ordinary  circumstances.  Suppose,  for  example,  that  the 
diameter  of  the  pupil  may  be  brought  from  4  to  8  millimeters.  The 
area  of  a  circle  being  expressed  by  r3*,  that  of  the  ordinary  pupil  is 
about  12  square  millimeters  and  that  of  the  dilated  pupil  about  50  square 
millimeters.  The  pupil  has  consequently  increased  by  38  square  milli- 
meters, or  about  three  times  its  size.  Thus  much  more  light  enters 


130  PHYSIOLOGIC  OPTICS 

through  these  peripheral  parts;  and  it  is  not  surprising  that  this  fact 
greatly  influences  the  answers  of  the  patient.  All  the  observations  of 
a  change  of  astigmatism  after  instilling  atropine  prove  nothing,  there- 
fore, in  favor  of  astigmatic  accommodation.  It  has  been  proposed  to 
study  the  question  by  placing  before  the  eye  a  diaphragm  of  the  size 
of  the  undilated  pupil,  but  I  do  not  see  how  we  could  assure  ourselves 
whether  the  position  of  the  diaphragm  really  corresponded  with  that  of 
the  undilated  pupil.  —  The  only  observations  in  favor  of  astigmatic 
accommodation  which  could  lay  claim  to  some  value,  are  those  in  which 
the  observer,  provided  with  a  weak  cylinder,  begins  by  seeing  distinctly 
one  line  of  the  star  figure  and  ends  by  seeing  all  with  the  same  distinct- 
ness. But  the  observations  of  this  kind  which  have  been  published  are 
by  no  means  beyond  all  criticism.  If  any  one  desires  to  again  perform 
this  experiment  he  had  better  use  a  luminous  point :  after  having  placed 
a  weak  cylinder  before  the  eye,  it  would  be  necessary  to  observe  the 
different  forms  under  which  the  luminous  point  would  be  seen  at 
different  distances  (see  the  following  chapter)  and  to  repeat  this  exam- 
ination after  having  worn  the  cylinder  for  an  hour  or  two,  to  see  if  the 
figures  had  undergone  any  change. 

The  alleged  astigmatic  accommodation  was  always  of  a  very  low  de- 
gree, i  D.  to  1.5  D.  at  most.  Frequently,  in  order  to  discover  it,  a  very 
persistent  atropinization  was  necessary,  lasting  as  much  as  fifteen  days 
and  even  until  symptoms  of  poisoning  appeared.  I  think  that  frequently 
the  patient,  weary  of  the  struggle,  ended  by  answering  all  that  was 
desired. 

71.  Post-operative  Astigmatism.  —  If  we  examine  the  cornea  eight 
days  after  the  extraction  of  a  cataract,  we  find  an  enormous  astigmatism 
against  the  rule,  sometimes  reaching  12  or  14  D.  The  vertical  meridian 
is  flattened,  probably  in  consequence  of  the  interposition  of  an  exuda- 
tion between  the  lips  of  the  wound;  the  phenomenon  is  more  pro- 
nounced if  there  exists  a  hernia  of  the  iris.  This  astigmatism  diminishes 
gradually;  it  may  disappear  altogether,  but  generally  one  or  two  diop- 
trics remain.  For  this  reason  it  is  prudent  to  postpone  the  selection  of 
spectacles  for  two  or  three  months  after  the  extraction,  or,  if  the  patient 
desires  to  have  them  immediately,  to  warn  him  that  it  will  be  necessary 
to  change  them  after  two  months.  Contrary  to  what  we  would  expect, 
the  agreement  between  the  subjective  astigmatism  and  the  ophthalmo- 
metric  measurement  is  less  than  for  the  normal  eye,  which  is  due  partly 
to  the  distance  of  the  correcting  glass  from  the  eye  (see  page  128), 


REGULAR  ASTIGMATISM 


131 


partly  to  the  fact  that  the  cornea  very  frequently  retains  a  certain  de- 
gree of  irregularity  after  extraction.  What  we  have  said  of  the  extrac- 
tion of  cataract  applies  also,  but  in  a  much  less  degree,  to  iridectomy  and 
other  operations  performed  on  the  cornea. 

72.  Keratoconus.  —  Apart  from  post-operative  cases,  we  meet  the 
highest  degrees  of  corneal  astigmatism  in  cases  of  keratoconus.  (i)  The 
apex  of  the  cone  does  not  generally  coincide  with  the  visual  line,  which 
gives  rise  to  a  strong  astigmatism,  the  direction  of  which  varies,  follow- 
ing the  direction  of  the  apex  of  the  cone.  We  observe  at  the  same  time 
that  the  images  of  the  mires  are  very  irregular.  By  removing  the  prism 
and  placing  the  keratoscopic  disc  in  its  place,  we  easily  find  the  direction 
of  the  look  which  brings  the  apex  of  the  cone  into  the  axis  of  the 
ophthalmometer ;  we  then  see  the  image  of  the  keratoscopic  disc  quite 
small  and  frequently  regular,  round  or  oval ;  in  every  other  position  its 


Fig.  84.  —  Keratoscopic  images  of  a  case  of  keratoconus. 

form  is  ovoid  (fig.  84).  —  The  cases  which  Javal  had  first  described 
under  the  name  of  decentered  eyes,  because  he  thought  their  deformity 
depended  on  an  unusual  size  of  the  angle  «,  were  affected  with  a  light 
degree  of  keratoconus,  as  he  has  since  acknowledged.  Outside  of  cases 

(1)  The  expression  "keratoconus"  is  not  very  happy ;  the  form  of  the  cornea  approaches  in  these 
cases  that  of  a  hyperboloid ;  we  know,  indeed,  that  this  body  closely  resembles  a  cone  with  rounded 
apex. 


132  PHYSIOLOGIC  OPTICS 

of  keratoconus,  we  quite  frequently  meet  cases  in  which  the  images  of 
the  mires  or  of  the  keratoscopic  disc  present  more  or  less  pronounced 
irregularities,  for  example,  in  consequence  of  old  lesions  of  the  cornea. 
Frequently,  however,  we  still  succeed  in  making  an  ophthalmometric 
measurement  which  may  give  information  useful  for  the  choice  of  a 
cylinder. 

73.  Symptoms  of  Astigmatism.  —  The  most  important  symptom  of 
astigmatism  is  the  diminution  of  visual  acuity,  which  is  a  consequence 
of  the  want  of  distinctness  of  the  image.  Generally  the  images  are  a 
little  deformed,  but  astigmatic  patients  are  accustomed  to  this  deformity 
and  take  no  notice  of  it. 

ASTHENOPIA  OF  ASTIGMATIC  PATIENTS.  —  On  account  of  their  dimin- 
ished acuity  astigmatic  persons  are  obliged  to  bring  objects  near  them 
for  the  purpose  of  obtaining  larger  retinal  images.  They  are,  therefore, 
obliged  to  accommodate  more  than  other  persons,  which  is  in  itself  a 
cause  of  astigmatism.  But  there  are  yet  other  reasons  for  it. 

It  may  be  asked  how  astigmatic  persons  see,  that  is  to  say,  what  part 
of  the  interfocal  distance  is  it  that  they  bring  preferably  on  the  retina. 
Following  Sturm  it  was  believed  that,  in  cases  in  which  they  have  their 
choice,  they  prefer  to  use  the  circle  of  diffusion  so  as  to  see  all  the  out- 
lines with  the  same  degree  of  confusion.  According  to  later  researches 
(Javal)  it  is  the  vertical  focal  line  that  they  use  preferably.  There  are 
several  reasons  for  this  preference :  one  is  that  it  is  much  more  import- 
ant in  reading  to  see  the  vertical  lines  distinctly,  the  legibility  of  the 
letters  depending  especially  on  the  distinctness  with  which  the  vertical 
lines  are  seen.  Another  reason  is  the  importance  which  vertical  out- 
lines have  for  binocular  vision.  If  one  sees  only  the  horizontal  lines, 
there  is  nothing  to  indicate  for  what  distance  the  eyes  must  converge. 
For  want  of  being  able  to  use  the  vertical  focal  line  astigmatic  persons 
have  recourse  to  the  horizontal  line,  but  very  rarely  to  the  intermediary 
part. 

In  cases  of  astigmatism  with  the  rule,  the  degree  of  accommodation  to 
be  used  depends,  therefore,  on  the  meridian  of  least  refraction.  Any 
one  having  compound  hypermetropic  astigmatism,  simple  hyperme- 
tropic  astigmatism  or  mixed  astigmatism  is,  therefore,  in  the  same 
situation  as  a  hypermetrope ;  he  has  the  same  reasons  for  having  accom- 
modative asthenopia.  Persons  having  myopic  astigmatism  with  the 
rule  or  against  the  rule  (if  it  is  not  combined  with  hypermetropia)  have 
Jess  cause  to  suffer  from  asthenopia  and  seem,  indeed,  to  suffer  less. 


REGULAR  ASTIGMATISM  133 

George  Bull  especially  has  laid  stress  on  this  explanation  of  the  asthenopia 
of  astigmatic  persons. 


74.  Examination  of  Astigmatic  Persons.  —  When,  on  examining  the 
patient  with  spherical  glasses,  we  do  not  find  a  satisfactory  acuity  we 
suspect  astigmatism,  unless  the  explanations  of  the  patient  give  reason 
to  suspect  an  internal  disease  of  the  eye.  We  then  submit  the  patient 
to  ophthalmometric  examination,  which,  according  to  the  rules  that  .we 
have  laid  down,  gives  an  approximate  idea  of  the  direction  and  degree 
of  the  subjective  astigmatism.  If  we  find  a  very  low  degree  with  the 
ophthalmometer  we  may  generally  come  to  the  conclusion  that  the 
complaints  of  the  patient  need  not  be  attributed  to  astigmatism.  We 
then  pass  to  the  subjective  examination;  we  make  the  patient  myopic 
two  or  three  dioptrics  and  move  the  star  figure  close  enough  for  him 
to  see  one  of  the  lines  distinctly.  Under  these  circumstances,  the  patient  sees 
distinctly  the  line  which  corresponds  to  the  meridian  of  greatest  refraction. 
The  direction  of  this  line  indicates,  therefore,  the  direction  of  the  axis 
of  a  convex  cylinder ;  a  concave  cylinder  must  be  placed  perpendicularly 
to  this  direction.  It  is  rare  to  find  an  appreciable  difference  between  the 
direction  indicated  by  the  ophthalmometer  and  that  thus  found,  unless 
in  the  case  of  a  very  slight  ophthalmometric  astigmatism  which  can  have 
no  bearing,  in  its  position  and  value,  on  the  total  astigmatism.  We 
may  then  proceed  to  find  the  cylinder  which  equalizes  all  the  lines,  but 
the  simplest  way  is  to  find  directly  the  cylinder  which  gives  the  best 
visual  acuity:  we  place  before  the  eye  the  glass  which  corrects  the 
spherical  ametropia,  joining  thereto  the  cylinder  indicated  by  the 
ophthalmometer,  in  the  position  found  by  means  of  the  star  figure. 
After  having  found  how  much  the  visual  acuity  is  thus  improved,  we 
try  whether  a  further  improvement  is  obtained  by  making  the  glass 
rotate  slightly  in  both  directions  and  adding  a  +  I  and  —  I  cylinder, 
being  very  careful  to  place  the  axis  of  the  glass  parallel  to  that  which  is 
already  in  the  frame.  According  as  the  acuity  gains  by  adding  a  one 
dioptry  convex  or  concave  cylinder,  we  replace  the  glass  of  the  frame 
by  the  following  number,  and  recommence  the  examination.  With 
patients  who  are  good  observers,  or  when  the  astigmatism  is  slight,  we 
may  sometimes  reach  a  greater  degree  of  accuracy,  by  using  a  half- 
dioptry  cylinder.  When  we  have  found  the  weakest  cylinder  which  gives 
the  best  visual  acuity,  we  verify  the  spherical  glass  by  adding  a  +  i 
spherical  which  ought  to  diminish  the  visual  acuity  and  a  —  I  spherical 
which  ought  not  to  increase  it. 


134  PHYSIOLOGIC  OPTICS 

After  having  made  the  subjective  examination,  we  examine  the  patient 
with  the  ophthalmoscope.  I  will  mention  farther  on  the  ophthalmo- 
scopic  signs  of  astigmatism  on  which  great  stress  was  laid  at  a  time 
when  there  were  no  other  objective  signs  of  this  anomaly;  they  have 
become  to-day  almost  mere  curiosities,  especially  since  skiascopy  has 
assumed  a  merited  importance.  When  we  make  use  of  it  for  verifica- 
tion, we  place  the  correcting  glass  in  a  frame  and  examine  by  skiascopy 
whether  the  correction  is  complete.  We  can  also  use  it  to  find  out  the 
direction  of  the  axis  and  the  value  of  the  astigmatism,  if  we  have  no 
ophthatmometer. 

Skiascopy  with  a  luminous  point  especially  enables  us  to  find  very 
exactly  the  direction  of  the  axis  by  means  of  the  luminous  band,  men- 
tioned on  page  118.  In  order  that  the  phenomenon  may  be  distinct  it  is 
necessary  that  the  eye  of  the  observer  be  placed  in  one  of  the  focal  lines, 
and  that  the  mirror  forms  the  image  of  the  luminous  source  at  the  place 
of  the  other  focal  line.  The  observer  will  then  see  luminous  the  meri- 
dian at  the  focus  of  which  he  is.  Thus  if  the  observed  eye  has  a  myopia 
of  2  D.,  combined  with  an  astigmatism  with  the  rule  of  2  D.,  he  will  see 
a  horizontal  luminous  band  if  he  is  placed  at  50  centimeters  and  illumi- 
nates the  eye  with  a  concave  mirror  which  projects  the  image  of  the 
luminous  source  at  25  centimeters.  To  see  the  band  vertical  he  must 
place  himself  at  25  centimeters  and  examine  with  a  plane  mirror.  —  Gen- 
erally it  is  necessary  to  dilate  the  pupil. 

There  are  two  points  in  particular  on  which  I  would  lay  great  stress. 
First,  the  importance  of  the  subjective  examination  which  must  always 
have  the  last  word ;  it  is  only  in  cases  in  which  it  is  impossible  to  obtain 
information  from  the  patient,  that  we  can  attempt  to  give  correcting 
glasses  according  to  the  data  furnished  by  the  objective  methods.  The 
reason  is  that,  in  most  cases,  the  correction  of  the  eye  by  a  cylinder 
is  not  a  simple  optic  problem.  Most  frequently  the  astigmatism  is  not 
the  same  in  the  entire  pupillary  space;  that  of  the  exterior  zones  differs 
more  or  less  from  that  of  the  central  zones;  the  best  correcting  glass 
is  only  a  sort  of  guess,  which  neither  the  ophthalmometer  nor  skiascopy 
can  assume  to  indicate  exactly.  It  is  well  understood  that  these  differ- 
ences are  usually  not  great,  especially  in  the  case  of  persons  who  consent 
to  the  correction,  but  they  suffice,  however,  to  make  the  subjective 
examination  indispensable. 

The  other  point  which  I  would  emphasize  is  that  the  prescribing  of 
cylinders  should  not  be  abused.  Since  the  invention  of  the  ophthalmo- 
meter there  is  too  decided  a  tendency  to  prescribe  cylinders  as  soon 


REGULAR  ASTIGMATISM  135 

as  a  diagnosis  of  astigmatism  is  made.  'Cylindrical  glasses  should  not, 
in  my  opinion,  be  prescribed  unless  they  produce  a  palpable  improve- 
ment of  the  visual  acuity ;  the  wearing  of  glasses  is  always  an  annoyance 
for  the  patient,  and  cylindrical  glasses  more  so  than  any,  as  well  on 
account  of  the  difficulty  of  wearing  them  in  eye-glasses  as  on  account  of 
the  errors  in  the  direction  of  the  axis  which  opticians  sometimes  com- 
mit, the  difficulty  of  replacing  a  broken  glass,  etc. 

If  there  are  several  cylinders  which  give  the  same  acuity  it  is  best  to 
choose  the  weakest.  If  there  is  astigmatism  of  only  one  eye,  we  may 
allow  the  patient  to  say  whether  he  will  have  it  corrected  or  not;  gen- 
erally he  does  not  gain  much  by  the  correction  except  in  cases  where 
there  is  a  tendency  to  strabismus. 

If  we  combine  two  cylinders  of  the  same  strength  by  placing  the  axes 
parallel,  they  act  like  a  cylinder  twice  as  strong;  if  we  place  the  axes 
perpendicularly  to  each  other,  they  act  like  a  spherical  glass,  and  if  the 
axes  form  an  acute  angle  with  each  other  the  effect  is  the  same  as  that 
of  a  sphero-cylindrical  combination,  the  spherical  and  cylindrical 
strength  of  which  vary  with  the  angle.  As  we  can  obtain  no  other  effect 
with  two  cylinders  than  with  one  cylinder  combined  with  a  spherical 
glass,  the  bi-cylindrical  glasses  are  now  abandoned. 

The  variable  cylindrical  lens  of  Stokes  was  composed  of  one  cylinder 
which  remained  fixed  and  another  which  could  be  rotated ;  we  thus  ob- 
tained a  variable  cylindrical  effect,  but  the  instrument  had  this  disad- 
vantage that  the  direction  of  the  axis  varied  also.  Javal  remedied  this 
by  making  the  two  cylinders  rotate  in  opposite  directions ;  but,  in  spite 
of  this  improvement,  the  lens  of  Stokes  has  never  been  of  any  practical 
utility,  because  of  the  spherical  effect  which  varies  at  the  same  time  as 
the  cylindrical,  (i) 

We  can  always  obtain  the  effect  of  a  given  sphero-cylindrical  combina- 
tion with  the  cylinder  of  contrary  sign,  by  changing  the  spherical  glass. 
A  +  5  spherical  combined  with  a  +  3  cylindrical  is  thus  equivalent  to  a 
H-  8  spherical  with  a  —  3  cylindrical.  Really,  there  is  need,  therefore, 
of  only  one  kind  of  cylinder ;  there  is  also  now  a  tendency  to  prescribe 
only  concave  cylinders  which  are  combined  with  convex  sphericals  to 
obtain  the  effect  of  convex  cylinders.  By  placing  the  cylinder  on  the 
side  of  the  eye  we  thus  obtain  a  slight  periscopic  effect. 

Periscopic  glasses,  which  were  invented  by  Wollaston,  are  concavo- 


(1)  [This  last  defect  has  been  overcome  in  the  optometer  of  the  translator.  In  this  instrument  two 
spherical  lenses  are  so  moved  that  the  spherical  effect,  produced  by  the  rotation  of  the  two  cylinders,  is 
always  neutralized  by  the  contrary  spherical  effect  of  the  two  spherical  lenses.  Thus  a  purely  cylin- 
drical action  is  obtained.  See  Annals  of  Ophthalmology,  Vol.  Ill,  No.  1.]  —  It'. 


136  PHYSIOLOGIC  OPTICS 

convex  menisci  the  concave  side  of  which  is  next  the  eye.  Their  ad- 
vantage consists  in  this  that  the  peripheral  parts  of  the  visual  field  appear 
more  distinct  because  the  rays  pass  through  the  glasses  less  obliquely 
than  in  the  ordinary  case.  This  advantage  also  exists  when  the  eye  is 
motionless  as  regards  the  peripheral  directions  of  the  look.  For  some 
time  the  attempt  has  been  made  to  replace  cylindrical  glasses  by  toric 
glasses,  one  of  the  surfaces  of  which  is  cut  as  a  tore,  the  other  as  a 
spherical  surface.  They  have  the  advantage  of  being  periscopic,  but 
their  manufacture  is  difficult  and  up  to  the  present  they  are  not  very 
popular. 

Cases  of  exact  correction  of  astigmatism  are  among  the  most  agree- 
able which  the  oculist  can  meet,  and  it  happens  quite  frequently  that  a 
normal  acuity,  or  even  higher  than  normal,  may  be  obtained.  Frequently 
the  acuity  remains  under  the  normal,  and  there  is  a  certain  number  of 
cases  in  which  the  effect  of  the  glasses  is  nil  or  nearly  so.  Oculists  are 
not  in  agreement  as  to  the  number  of  cases  in  which  a  good  result  may 
be  obtained.  Schweigger  says  that,  in  a  considerable  minority  of  cases 
of  astigmatism  the  correction  obtained  by  cylinders  is  quite  satisfac- 
tory. Other  authorities  are  less  pessimistic. 

Bibliography.  —  (Euvres  de  Young,  edited  by  Tscherning,  p.  125.  —  Airy.  Transactions 
of  the  Cambridge  Phil.  Soc.,  1827,  t.  II  et  1849,  t.  VIII.  —  Sturm.  Sur  la  theorie  de  la  vision. 
Reports,  1845.  —  Goulier.  Sur  un  defaut  assez  commun  de  conformation  des  yeux  et  sur  les  mo- 
yens  de  rendre  la  vue  distincte  aux  personnes  qui  en  sont  atteintes.  Reports,  1865.  —  Knapp  (H.). 
Ueber  die  Asymmetrie  des  Auges  in  seinen  verschiedenen  Meridiansystemen.  Arch.f.  Ophth.,  VIII, 
2,  p.  185.  —  Donders  (F.  C.).  Astigmatwnus  und  cylindrische  Qldser.  Berlin,  1862.  —  Javal 
(E.)  in  de  Wecker.  Traite  des  maladies  des  yeux,  II,  Paris,  1863.  —  Javal  (E.)«  Sur  le  ehoix 
des  verres  cylindriques,  Ann.  d'oc.,  1863.  —  Javal  (E.).  Memoires  dj opJitalmometrie.  Paris, 
1891.  —  Schioetz  (H.).  Ophtalmometrische  und  optometrische  Untersuchung  von  969  Augen. 
Arch.f.  Augenh.,  1885.  —  Nordenson  (E. ).  Recherches  ophtalmometriques  sur  I'astigmatisme  de 
la  cornee.  Ann.  d'oc.,  1883.  —  Bull  (G.).  L'asthenopie  des  astigmates.  Bull,  de  la  Soc.  fran9. 
d'ophtal.,  1892,  p.  128. 


CHAPTER  X. 

IRREGULAR  ASTIGMATISM. 

75.  General  Bemarks.  —  When  we  do  not  succeed  in  obtaining  a 
normal  visual  acuity  by  means  of  spherical  and  cylindrical  glasses,  we 
generally  attribute  the  cause  of  this  failure  to  the  retina — we  diagnose 
amblyopia.  —  Sometimes,  but,  as  a  rule,  quite  rarely,  the  diminution 
of  visual  acuity  is  attributed  to  an  irregular  astigmatism,  especially  if  it 
is  visible  by  the  deformities  of  the  ophthalmoscopic  or  skiascopic  images. 
But  it  is  probable  that  the  more  we  will  study  the  optics  of  the  eye, 
the  more  the  diagnosis  of  amblyopia  will  give  place  to  that  of  irregular 
astigmatism,  which  has  served  up  to  the  present  as  the  common  term 
for  all  optic  defects  of  the  eye  other  than  myopia,  hypermetropia  and 
regular  astigmatism,  that  is  to  say,  those  which  we  can  correct  with 
test  case  lenses.  For  some  time  past  the  majority  of  works  which  have 
been  published  on  the  optics  of  the  eye,  have  had  for  their  object  the 
improvement  of  the  methods  used  to  determine  these  defects  as  quickly 
and  as  exactly  as  possible.  There  is  little  probability  that  we  can,  for 
the  moment,  make  progress  of  any  importance  in  this  direction;  these 
methods  are,  at  present,  very  well  developed ;  it  even  seems  to  me  that 
we  bid  fair  to  overstep  the  limit,  in  this  sense  that  we  can  perceive  a 
tendency  to  desire  to  determine  these  defects  too  exactly.  Quarters 
of  a  dioptry  are,  indeed,  superfluous  for  our  test  cases,  and  even  half 
dioptrics  are  only  rarely  indispensable,  except  for  very  weak  ametropias. 
So  long  as  it  was  supposed  that  the  refraction  was  the  same  in  the  whole 
pupillary  space,  we  could  imagine  the  possibility  of  determining  this 
refraction  with  great  exactness.  But  since  we  know  that  there  are  in 
nearly  all  eyes  optic  differences  between  the  different  parts  of  the  pupil- 
lary space,  and  since  these  differences  may  reach  several  dioptrics,  the 
correcting  glass  must  be  regarded  as  a  sort  of  approximation  which 
we  cannot  determine  with  perfect  exactness.  It  seems  that  the  con- 
struction of  the  eye  is  such,  that  the  visual  acuity  is  about  2  for  a  perfect 

137 


138  ,  PHYSIOLOGIC  OPTICS 

optic  system;  but  many  eyes  have  optic  irregularities  which  lower  the 
acuity  to  i,  to  five-sixths,  to  three-fourths  or  still  lower,  and  these 
irregularities  are  frequently  still  more  pronounced  in  astigmatic  eyes, 
which  prevents  complete  correction. 

The  study  of  these  irregularities  seems,  therefore,  destined  to  play 
a  certain  part  in  future  works  on  the  optics  of  the  eye.  As  I  have  already 
remarked,  we  can  study  them  with  the  keratoscopic  disc  of  the  Javal 
and  Schioetz  ophthalmometer,  and  we  can  measure  them  with  the  opto- 
meter  of  Young,  which  necessitates,  however,  on  the  part  of  the  ob- 
server a  certain  amount  of  work  to  accustom  himself  to  the  instrument. 
But  the  best  means  of  studying  these  irregularities  is  the  following. 

76.  Examination  of  the  Eye  with  a  Luminous  Point.  —  We  have  already 
seen  that  the  first  authors  who  devoted  their  attention  to  the  question 
of  regular  astigmatism,  used  the  luminous  point  to  find  the  meridians 
and  to  judge  of  the  exactness  of  the  correction.  Later,  the  luminous 
point  was  replaced  by  the  star  figure,  which  is  in  more  common  use  for 
finding  the  meridians,  but  which  gives  information  only  on  the  astig- 
matism which  can  be  corrected  by  a  cylindrical  glass.  The  forms  under 
which  a  luminous  point  is  seen  furnish,  on  the  contrary,  fuller  informa- 
tion: there  is  no  optic  defect  of  the  eye  which  is  not  shown  in  these 
figures,  sometimes,  it  is  true,  under  a  form  which  it  may  be  difficult  to 
interpret.  This  is  why  we  have  undertaken  this  examination  at  the 
laboratory  of  Sorbonne.  As  object  we  use  a  very  small  opening  (0.2  mm. 
to  0.3  mm.),  made  in  a  dark  screen,  and  on  which  is  concentrated  the 
light  of  a  lamp  or  daylight.  The  patient,  rendered  myopic,  gradually 
approaches  the  luminous  point  while  observing  the  form  under  which 
the  latter  may  appear.  We  can  also  place  the  patient  at  a  fixed  distance, 
at  one  meter,  for  example,  and  virtually  change  the  distance  of  the 
luminous  point  by  placing  concave  or  convex  glasses  before  the  eye; 
the  patient  must  avoid  as  much  as  possible  using  his  accommodation. 
We  can  thus  examine  the  form  of  the  refracted  pencil  throughout  its 
whole  extent,  for,  as  far  as  the  question  at  issue  is  concerned,  it  amounts 
to  the  same  whether  the  luminous  point  be  fixed  while  the  retina  is  dis- 
placed, or  whether,  the  retina  being  fixed,  we  displace  the  luminous 
point.  Most  of  the  time  the  patient  sees  circles  of  diffusion  presenting 
pretty  exactly  the  form  of  the  pupil,  which  diminishes  according  as  the 
luminous  point  approaches  the  focus.  But  near  the  latter,  in  front  and 
behind,  there  is  a  part,  the  characteristic  part  of  the  pencil,  where  the 
circle  assumes  irregular  forms.  The  round  diffusion  spots  are  alike  in 


IRREGULAR  ASTIGMATISM  139 

all ;  at  most  we  find  some  slight  differences  due  to  the  form  of  the  pupil, 
to  a  different  distribution  of  the  brightness  of  the  circles,  or  to  entoptic 
phenomena  which  I  shall  describe  in  the  following  chapter.  But  the 
characteristic  part  of  the  pencil  differs  so  much  in  different  persons  that 
I  have  never  met  two  eyes  in  which  it  was  alike,  except,  perhaps,  in  the 
two  eyes  of  the  same  person. 

77.  Different  Forms  of  Irregular  Astigmatism.  —  We  can  distinguish 
several  groups: 

i°  In  an  ideal  eye  the  characteristic  part  of  the  pencil  is  reduced  to  a 
point.  We  sometimes  meet  eyes  which  do  not  differ  much  from  this 
type,  but  they  are  rare,  and  all  have  an  exceptional  visual  acuity  (fig. 
85).  (i)  It  is  besides  clear  that,  all  things  equal,  the  better  the  eye  the 
shorter  the  characteristic  point  of  the  pencil. 


Fig.  85.  —  Forms  under  which  a  luminous  point  is  seen  by  a  regular  eye.    After  Ree. 

2°  Eyes  regularly  astigmatic  should  see  figures  similar  to  those  of 
figure  77,  but  eyes  so  regular  scarcely  exist.  In  low  degrees  of  astigma- 
tism we  scarcely  ever  have  distinct  focal  lines,  and  in  strong  degrees, 
where  the  focal  lines  are  clearer,  irregularities  appear  when  the  astig- 
matism is  approximately  corrected  by  a  cylinder.  The  most  regular 


(1)  Figures  85,  86,  87,  89,  90,  91,  92  are  borrowed  from  a  work  which  M.  R6e  compiled  at  the  laboratory 
of  the  Sorbonne  (  Undersoegelse  of  Oeiet  med  et  lysende  Punct,  Copenhagen,  1896)  and  which  has  the  shape 
of  a  small  atlas  showing  the  forms  under  which  the  eye  sees  a  luminous  point.  But  the  question  is  far 
from  being  exhausted,  and  it  would  be  desirable  that  some  one  should  again  take  it  up  in  a  clinic. 
With  some  exceptions,  the  eyes  of  the  persons  examined  by  M.  Ete  were  what  we  call  normal  eyes ; 
but  it  is  especially  astigmatic  persons,  whose  vision  does  not  improve  with  cylinders,  that  should  be  ex- 
amined. 


140 


PHYSIOLOGIC  OPTICS 


astigmatic  patients  frequently  see  forms  analogous  to  those  of  figure  86. 
The  focal  lines  are  thicker  at  the  middle  and  the  interfocal  diffusion  spot 


Fig.  86.  —  Regular  astigmatism  with  spherical  aberration.     After  Ret. 

is  not  circular,  but  in  the  form  of  a  lozenge.    These  forms  are  due  to 
the  combination  of  a  regular  astigmatism  with  a  quite  pronounced 


Fig.  87.  —  Figures  of  a  luminous  point  obtained  by  combining  an  ordinary  strong  spherical 
lens  with  a  cylindrical  lens  (astigmatism  with  spherical  aberration).  After  Ree. 

spherical  aberration,  for  we  can  obtain  forms  wholly  analogous  with  a 
combination  of  a  +  20  sph.  with  a  -f-  6  cyl.  of  our  test  cases  (fig.  87). 


IRREGULAR  ASTIGMATISM 


141 


It  is  for  this  reason  that  one  is  obliged  to  use  an  aplanatic  lens  to  ob- 
tain figures  of  pure  astigmatism.     In  the  more  irregular  eyes  we  can 

a  b  c  d 


B 


Fig.  88.  —  A,  forms  which  a  luminous  point  presents  to  my  right  eye  (obliquity  in  one 
meridian,  the  vertical).  —  B,  appearance  of  the  same  figures  if  I  cover  the  lower  half 
of  the  pupil.  —  C,  appearance  of  the  figures  if  I  cover  the  upper  half  of  the  pupil. 

The  figures  a  correspond  to  a  distance  of  60  centimeters;  the  figures  b  to  1  meter; 
the  figures  c  to  1.50m  and  the  figures  d  to  infinity. 

generally  find  figures  which  represent  more  or  less  perfectly  the  focal 
lines,  that  is  to  say,  there  are  two  places  where  the  figures  are  more 


Fig.  89.  —  Eye  with  double  obliquity.   After  Ree. 

or  less  elongated,  so  that  their  two  long  axes  are  perpendicular  to  each 
other;  but  these  figures  are  far  from  being  linear. 


142 


PHYSIOLOGIC   OPTICS 


Fig.  90.  —  Figures  of  the  left  eye  of  M.  Eee  (Obliquity  in  one  meridian,  the  vertical). 

Curved  focal  line. 


Fig.  91.  —  Curved  focal  line.   After  Eee. 


IRREGULAR  ASTIGMATISM  143 

3°  It  is  not  rare  for  the  optic  system  of  the  eye  to  affect  a  certain 
obliquity,  so  that  the  figures  are  symmetrical  in  relation  to  a  single  axis 
(and  not  in  relation  to  two  axes,  as  in  regular  astigmatism).  It  is  so  in 
the  case  of  my  right  eye  (fig.  88)  and  also  in  that  of  M.  Ree  (fig.  90). 
These  figures  are,  up  to  a  certain  point,  analogous  to  those  which  are 
obtained  with  a  lens  placed  obliquely. 

4°  Frequently  we  discover  an  obliquity  in  the  two  directions  per- 
pendicular to  each  other,  so  that  the  figures  are  not  symmetrical  at  all 

(fig.  89). 

5°  An  anomaly  which  is  not  at  all  rare  consists  in  a  certain  curvature 
of  the  focal  lines,  due  probably  to  the  fact  that  the  principal  meridians 
of  the  cornea  show  an  analogous  curvature  (figs.  90,  91). 


Fig.  92.  —  Irregular  eye  (Diplopia).  After  Ree. 

6°  We  quite  frequently  meet  more  irregular  figures,  those  for  in- 
stance of  figure  92,  belonging  to  an  eye  which  has  a  rather  pronounced 
diplopia. 

78.  Rules  for  Analyzing  the  Figures  of  the  Luminous  Point.  —  The 
figures  are  sometimes  quite  difficult  to  analyze.  Here  are  some  di- 
rections for  this  analysis: 

i°  We  can  always  decide  whether  a  part  of  a  figure  is  formed  by 
crossed  rays  or  not,  by  covering  a  part  of  the  pupil.  If  it  is  the 


144  PHYSIOLOGIC  OPTICS 

homonymous  part  of  the  figure  which  disappears,  this  part  is  formed 
by  rays  which  have  already  crossed  the  axis  before  reaching  the  retina; 
if  it  is  the  heteronymous  part  which  disappears,  the  rays  have  not  yet 
crossed  the  axis.  —  Sometimes  we  can  with  advantage  use  cobalt  glass 
(see  page  112)  for  this  analysis. 

2°  If  the  luminous  point  is  beyond  the  punctum  remotum,  and  if  the 
observer  notices  a  concentric  brightness  on  a  part  of  the  diffusion 
spot,  this  part  corresponds  to  a  less  refracting  part  than  the  remainder 
of  the  pupil ;  for,  the  focus  of  this  part  is  nearer  the  retina  and  its  rays 
are,  consequently,  less  dispersed. 

3°  If,  within  the  focus,  the  figures  are  elongated  in  one  direction, 
downwards  for  example,  they  are  elongated  in  the  same  direction  beyond 
the  focus,  and  the  eye  is  more  refracting  in  this  direction.  Thus  in 
figure  95,  A,  in  which  the  lower  part  of  the  surface  is  supposed  to  be 
more  refracting,  the  part  of  the  cone  situated  above  the  axis  is  every- 
where larger.  The  diffusion  spots  are  seen  elongated  downward 
(fig.  88). 

4°  The  aberroscopic  phenomena  (page  102)  always  tell  us  in  what 
direction  the  refraction  increases  or  diminishes,  starting  from  the  center 
of  the  pupil. 

Finally  the  optometer  of  Young  permits  a  more  exact  analysis  of 
these  irregularities. 

Let  us  take,  for  example,  my  right  eye  (fig.  88),  and  see  how  we  can 
use  these  rules  to  analyze  the  figures.  We  observe  that  the  upper  part 
of  the  figure  d,  A,  seen  at  infinity,  has  a  greater  brightness  than  the 
lower  part.  On  covering  the  upper  half  of  the  pupil,  this  part  disap- 
pears, while,  if  we  cover  the  lower  half  of  the  pupil,  this  part  does  not 
change.  We  conclude  from  this,  following  rule  i°,  that  the  whole  figure 
is  formed  by  rays  that  have  crossed  the  axis,  that  is  to  say,  that  the 
whole  pupillary  space  is  myopic,  and,  following  rule  2°,  that  the  upper 
part  is  much  less  myopic  than  the  remainder.  —  If  I  move  nearer  up  to 
1.50  m.  from  the  luminous  point,  I  see  the  figure  c  which  resembles  a 
luminous  T  written  in  a  less  luminous  half  circle.  If  I  cover  the  upper 
half  of  the  pupil,  the  vertical  stroke  disappears  and  the  horizontal  stroke 
becomes  weaker.  We  conclude  from  this,  following  rule  i°,  that  the 
vertical  stroke  is  formed  by  rays  which  have  not  yet  crossed  the  axis. 
The  point  situated  at  1.50  m.  is,  therefore,  already  situated  within  the 


IRREGULAR  ASTIGMATISM 


145 


far  point  of  this  part,  while  it  is  situated  beyond  the  far  point  of  the 
lower  part.  All  the  figures  are  elongated  down- 
wards, which  also  shows  (following  rule  3°)  that  the 
pupil  is  more  refracting  below.  The  lines  of  the 
aberroscope  are  convex  towards  the  middle,  below 
and  towards  the  two  sides,  while  they  are  straight 
or  slightly  concave  towards  the  middle  above  (fig. 
93),  which  shows  that  the  refraction  diminishes 
towards  the  periphery  above  and  increases  in  the  Fig  93  _  Aberr08COpic 
three  other  directions.  —  Finally  we  find,  by  meas-  phenomena  of  my 
uring  with  the  optometer  of  Young,  the  refraction 
indicated  by  the  diagram  (fig.  94,  A).  The  measurements  confirm  the 
other  observations,  unless  it  be  that  they  disclose  a  slight  degree  of 
hypermetropia  near  the  upper  border  of  the  pupil,  which  had  escaped 
attention  in  the  analysis  of  the  figures.  It  follows  that  the  course  of 


Temporally 


Nasally    Temporally 


Nasally 


Fig.  94.  —  A,  Diagram  of  the  variations  of  refraction  in  the  pupil  (dilated)  of  my  right 
eye.  —  B,  diagram  of  the  refraction  in  the  pupil  of  Demicheri :  the  dotted  circle  indi- 
cates the  normal  pupil,  the  full  circle  the  dilated  pupil. 

the  rays  must  be  nearly  as  I  have  illustrated  them  in  figure  95 ;  A  cor- 
responds to  the  vertical  meridian,  B  to  the  horizontal  meridian;  the 
place  marked  2  corresponds  to  figure  88,  c. 

As  to  the  means  to  use  for  the  correction  of  these  defects,  they  still 
remain  to  be  discovered.  The  only  information  we  can  give  for  the 
present  is  that  the  forms  mentioned  under  rule  3°  could  probably  some- 
times be  corrected  more  or  less  effectively  with  glasses  placed  obliquely. 
—  Contact  glasses  could  evidently  correct  the  greater  part  of  these  de- 
fects, which  reside  especially  in  the  cornea.  As  the  cornea  scarcely 


146 


PHYSIOLOGIC  OPTICS 


tolerates  contact  Sulzer  caused  to  be  cut  similar  glasses,  which  are 
furnished  with  a  rim  by  which  they  are  supported  on  the  sclera.  Under 
this  form,  contact  glasses  are  easier  to  wear,  but  they  seem  nevertheless 


Fig.  95.  —  Course  of  the  rays  in  my  right  eye:  A,  in  the  vertical  meridian  (obliquity) 
B,  in  the  horizontal  meridian  (spherical  aberration). 

to  cause  a  certain  annoyance,  which  will  probably  prevent  their  use, 
except  in  special  cases. 

Bibliography.  —  Tscherning  (M.).  Die  monochromatischen  Abweichungen.  Zeitschri/t  f. 
Psych,  u.  Physiol.  der  Sinnesorg.,  IV,  p.  456.  —  Ke"e  (O.  M.).  Undersoegdse  of  Oeiet.  med  et 
lysende  Punkt.  (Danois).  Copenhagen,  1896. 


CHAPTER  XI. 

ENTOPTIC  PHENOMENA. 

79.  Manner  of  Observing  Entoptic  Phenomena.  —  When  we  approach 
a  luminous  point,  the  circle  of  diffusion  to  which  it  gives  rise  increases 
in  size.  At  the  moment  when  the  luminous  point  is  at  the  anterior  focus 
of  the  eye,  the  rays  are  parallel  after  refraction,  and  the  circle  of  diffu- 
sion is  the  size  of  the  pupil ;  on  approaching  nearer  to  it,  the  circle  still 
increases. 

In  these  circumstances  we  observe  entoptic  phenomena,  that  is  to  say, 
shadows  which  the  corpuscles  situated  in  the  refracting  media  of  the 
eye  project  on  the  retina.  If,  instead  of  a  point,  we  use  a  larger  luminous 
source,  the  cone  of  the  shadow  becomes  too  short  to  reach  to  the  retina, 
except  the  object  is  very  near  the  latter.  Another  way  of  observing 
entoptic  phenomena  consists  in  placing  ourselves  at  a  great  distance 
and  observing  the  luminous  point  through  a  strong  convex  lens.  In 
this  case  the  displacements  of  the  shadows  take  place  in  the  direction 
contrary  to  that  which  we  are  going  to  point  out  later.  —  Among  the 
entoptic  observations  I  shall  cite  the  following. 

i°  The  luminous  spot  is  limited  by  the  shadow  of  the  border  of  the 
iris ;  we  can  thus  study,  therefore,  the  irregularities  of  the  latter.  The 
pupillary  contraction  is  very  well  observed  on  opening  or  covering  the 
other  eye. 

2°  We  very  frequently  see  small  circles  the  centers  of  which  are 
bright,  and  which  have  an  apparent  motion  from  above  downwards, 
depending  on  the  winking  of  the  eyelids.  They  are  produced  by  small 
specks  on  the  anterior  surface  of  the  cornea,  and  which  move  in  a  con- 
trary direction  (fig.  96). 

3°  On  winking  the  eyes  we  produce  transverse  striae,  due  probably  to 
the  wrinkles  of  the  epithelial  layer.  If  we  wink  for  some  time,  for  ex- 
ample when  keeping  one  eyelid  closed  while  working  with  a  microscope, 
or  as  artists  frequently  do  in  order  to  obtain  a  better  idea  of  the  entire 

147 


148 


PHYSIOLOGIC  OPTICS 


impression  of  a  landscape,  we  can  produce  striae  which  last  for  several 
hours  and  give  rise  to  a  very  marked  diplopia  of  the  horizontal  lines 
(fig.  97).  George  Bull  especially  has  studied  this  question;  according  to 
him  the  phenomena  are  specially  pronounced  after  reading  for  a  long 


Fig.  96. 

After  Helmholtz. 


Fig.  97.  —  Striae  produced  by  winking 
the  eyelids.   (After  George  Butt.) 


time  in  the  horizontal  position,  and  give  rise  to  a  peculiar  annoyance 
which  he  has  named  tarsal  asthenopia. 

4°  On  winking  the  eyelids  while  looking  at  a  distant  luminous  point, 
we  observe  long  striae  which  run  upwards  and  downwards  from  the 
point.  These  striae  are  due  to  the  layer  of  tears  which  is  in  the  con- 
junctival  sac,  and  which,  near  the  border  of  the  eyelids,  assumes  the 
form  of  a  prism  with  a  concave  surface  (fig.  98).  This  prism  deflects 
the  rays  which  meet  it,  and,  as  its  surface  is  concave,  the  parts  placed 


Fig.  98.  —  Prismatic  effect  of  the  layer  of  tears. 

near  the  border  of  the  eyelid  act  as  a  stronger  prism,  which  causes 
greater  deflection  of  the  rays:  it  is  for  this  reason  that  we  see  a  stria 
and  not  simply  a  second  image  of  the  luminous  point.  The  upper  eyelid 
deflects  the  rays  upwards ;  it  produces,  therefore,  the  striae  which  we  see 
directed  downwards.  In  fact,  if  we  lower  a  screen  placed  near  the  eye, 
it  is  the  stria  directed  downwards  which  disappears  first.  This  phenom- 


ENTOPTIC  PHENOMENA 


149 


enon  is  not,  properly  speaking,  an  entoptic  phenomenon,  but  I  mention 
it  here  because  of  its  resemblance  to  those  mentioned  under  No.  3°. 

5°  If  we  rub  the  eye,  the  luminous  spot  presents  a  speckled  appear- 
ance, due  to  irregularities  of  the  cornea;  this  appearance  soon  disap- 
pears (fig.  99). 

6°  We  sometimes  observe  small  round  discs,  sometimes  bright  and 
surrounded  with  a  black  border,  sometimes  dark  with  a  bright  border, 
proceeding  from  the  crystalline  lens.  We  frequently  see  also  the  star 
figure  of  the  crystalline  lens,  sometimes  bright  (fig.  100),  sometimes 


Fig.  99.  —  Speckled  appearance  of  the  entoptic  Fig.  100. 

field  produced  by  rubbing  the  cornea.     (After  After  Helmholtz. 

George  Bull.) 

dark,  with  somewhat  more  luminous  borders.  The  crystalline  opacities 
are  outlined  in  the  spot  with  great  distinctness.  An  intelligent  patient 
can  thus  follow  step  by  step  the  development  of  his  cataract,  as  we  can 
see  on  the  drawings  which  M.  Daricr  has  just  published  (fig.  101). 

7°  Nearly  every  one  sees  objects  situated  in  the  vitreous  body;  they 
become  partly  visible  without  further  aid  by  simply  looking  at  the  sky, 

that  is  when  they  are  very  near  the  retina. 
They  are  sometimes  mobile,  sometimes  fixed, 
but  presenting  in  the  latter  case  an  apparent 
motion.  If,  for  example,  the  shadow  is  seen 
a  little  above  the  point  of  fixation,  the  patient 
looks  a  little  higher  in  order  to  fix  it;  but 
as  the  shadow  is  always  seen  above  the  point 
of  fixation,  it  continues  to  direct  the  visual 
line  higher  and  higher;  and  the  shadow 
always  flees  before  the  look,  for  which  reason 
the  name  muse  a  volitantcs  has  been  given  to 
this  phenomenon.  To  make  certain  whether 


Fig.  101.  —  Incipient  cata- 
ract, seen  entoptically. 
(After  Darier.) 


150 


PHYSIOLOGIC  OPTICS 


the  motion  is  apparent  or  real,  we  can  look  at  the  sky  through  a  window, 
on  which  we  select  a  mark  in  order  to  assure  fixation;  after  having 
made  a  rapid  movement  with  the  look,  we  fix  this  point.  If  the  cor- 
puscle is  fixed,  it  should  then  remain  motionless,  but  most  frequently 
we  see  it  descend  slowly  which  indicates  that  the  corpuscle  really 
ascends. 

8°  We  may  use  entoptic  observation  to  study  slight  displacements 
of  the  eye  as  a  whole,  which  it  is  very  difficult  to  observe  otherwise. 
To  this  end  I  have  had  constructed  a  small  instrument,  the  entoptoscope 
(fig.  ioia).  It  consists  of  a  small  plate  of  wood  which  we  take  between 

the  teeth;  on  the  plate  is  fixed  a  rod 
which  carries  a  plate  of  copper  having 
the  form  of  the  cap  of  a  sphere.  In 
the  middle  is  pierced  a  very  fine  open- 
ing (i/io  mm.),  which  is  on  a  level 
with  the  eye.  In  the  concavity  of  the 
cap  are  stretched  two  threads,  one  hor- 
izontal and  one  vertical,  placed  in  the 
form  of  a  cross  and  forming  cords  with 
the  cap.  When  we  take  the  instrument 
between  the  teeth  and  look  towards  the 
sky  we  see  the  entoptic  field  occupied 
by  the  cross  which  is  greatly  enlarged. 
We  select  a  point  in  the  cross  as  a  fixa- 
tion point.  The  position  of  the  cross 
is  thus  invariably  dependent  on  that  of 
the  head;  if  therefore,  in  given  circum- 
stances,  we  observe  a  displacement  of 
the  cross  in  the  entoptic  field,  it  is 
Because  it  is  the  latter,  that  is  to  say 

the  eye>  whlch  suffers  the  Displace- 
ment. We  can  thus  prove  that  the  eye 
is  slightly  displaced,  a  little  upwards  when  we  wink  the  eyelids,  a  little 
downwards  when  we  open  the  eye  very  widely.  When  we  lean  the 
head  to  one  side  the  eye  undergoes  a  slight  displacement  in  the  direction 
of  the  weight,  etc.  The  phenomena  are  especially  striking  when  we 
instil  eserine,  because  the  field  is  then  very  small.  The  displacement 
of  the  cross  may  then  reach  a  fourth  or  a  third  of  the  entire  extent  of 
the  field. 


Fig.  loio.  —  Entoptoscope.  a,  plan- 
chette  of  wood;  6,  rod:  c,  copper 
plate,  perforated;  4  thread. 


ENTOPTIC  PHENOMENA  151 

80.  Analysis  of  Entoptic  Phenomena. 

a).  OBSERVATION  OF  THEIR  PARALLAX  (Listing).  —  By  fixing  different 
points  of  the  entoptic  field,  we  observe  that  the  entoptic  phenomena  are 
displaced  in  the  field.  If  the  corpuscle  which  gives  rise  to  the  shadow 
is  behind  the  pupillary  plane,  the  shadow  moves  in  the  same  direction 


Fig.  102.  —  Parallax  of  the  entoptic  phenomena. 

as  the  visual  line  (fig.  102,  a,  b).  Taking  the  position  b,  the  visual  line 
is  directed  upwards;  the  shadow  has  descended  to  near  the  lower 
border  of  the  field,  but  seems  to  have  ascended  (by  the  projection  out- 
wards). It  is  easy  to  see  that  we  have  the  contrary  parallax  if  the 
object  is  in  front  of  the  pupillary  plane,  and  that  it  disappears  if  the 
object  is  in  this  plane.  As  the  movement  is  greater  in  proportion  as  the 
object  is  more  removed  from  the  pupillary  plane,  we  can  thus  form  an 
approximate  idea  of  the  position  of  the  corpuscle. 

b).  MEASUREMENT  OF  THE  DISTANCE  OF  THE  CORPUSCLE  FROM  THE 
RETINA  (Brewster,  Bonders  and  Doncan).  —  To  measure  this  distance 
Breivster  proposed  to  use  two  luminous  points.  We  then  see  two  circles 
of  diffusion  which  partly  overlap,  and  each  corpuscle  produces  two 
shadows.  We  measure  the  distance  between  the  two  shadows  of  the 
same  object  and  the  diameter  of  the  free  part  of  one  of  the  circles  DE 
(fig.  103) ;  the  ratio  between  these  two  measurements  is  equal  to  the 
ratio  between  the  distance  of  the  object  from  the  retina  and  that  of 
the  pupil  from  the  retina. 

Let  A  and  B  (fig.  103)  be  two  luminous  points  which  must  be  in  the 
anterior  focal  plane  of  the  eye,  d  the  middle  of  the  pupil,  o  the  object, 


152  PEJSIOLOaiC  OPTICS 

p  and  p!  the  shadows  and  c  and  q  the  centers  of  the  circles  ol  diffusion. 
Since  the  points  are  in  the  focal  plane,  dc  is  parallel  to  op  and  dc±  to  oplt 


Fig.  103.  —  Determination  of  the  position  of  an  entoptic  object.   After  Brewster. 

therefore:  "^  =  ^  >  anc*  figure  103  b  shows  that  cq  =  DE  =  R  -f-  «  if 
R  is  the  radius  of  the  circle  of  diffusion.  —  We  can  make  measurements 
by  using  as  a  luminous  source  a  sheet  of  white  paper  strongly  illumi- 
nated. We  look  through  two  stenopaic  openings  towards  this  sheet 
and  we  notice  the  places  where  the  shadows  are  projected  as  well  as  the 
borders  of  the  circles  (Bonders) .  Doncan  made  the  measurements  & 
double  vue  by  comparing  the  entoptic  phenomena  with  a  scale  seen  with 
the  other  eye. 

c).  EXAMINATION  OF  THE  REFRACTION  OF  THE  OBJECT.  —  So  far,  we 
have  treated  the  entoptic  phenomena  as  shadows,  and  the  objects  which 
produce  them  as  opaque  bodies.  Most  frequently,  this  is  not  the  case, 
as  they  are  more  or  less  transparent;  but  their  refraction  is  different 
from  that  of  the  surrounding  parts,  whether  their  surface  has  a  different 
curvature,  or  whether  their  index  is  different. 

It  is  easy  to  see  (fig.  104)  that  the  more  refracting  objects  must  con- 
centrate the  light  so  that  the  entoptic  image  becomes  luminous  and 
surrounded  by  a  dark  border;  this  is  the  case  with  the  images  of  the 
corneal  specks.  —  On  the  contrary,  if  the  object  is  less  refracting  than 
the  surrounding  parts,  the  image  is  dark,  with  a  more  luminous  border. 
The  difference  is  specially  marked  in  the  case  of  the  star  figure  of  the 
crystalline  lens,  which,  in  some  people,  appears  dark,  in  others  luminous, 
thus  indicating  that  the  refraction  of  the  corresponding  parts  is  some- 


ENTOPTIC  PHENOMENA  153 

times  greater,  sometimes  less  than  that  of  the  surrounding  parts.  —  If 
we  make  the  experiment  by  placing  ourselves  at  a  great  distance,  and 
making  the  eye  strongly  myopic,  we  should  have  the  phenomena  in- 
verted. 


Fig.  104.  —  The  drop  on  the  cornea  causes  convergence  of  the  rays  which  pass  through  it 
so  that  we  see  a  luminous  center  surrounded  by  a  shadow. 

In  the  experiment  which  we  have  just  noted  (fig.  104),  the  dark  border 
is  due  to  the  fact  that  part  of  the  rays  which  should  illuminate  it  are 
made  to  converge  towards  the  middle  of  the  entoptic  image,  by  the 
interposition  of  the  corpuscle.  This  border  is  always  diffuse  and  fre- 
quently somewhat  pronounced;  it  must  not  be  confounded  with  the 
diffraction  ring  which  surrounds  the  images  along  the  border  of  the 
pupil  when  the  luminous  point  is  very  small.  This  ring,  which  some- 
times may  be  double  or  triple,  is  always  very  thin  and  very  distinct. 

81.  Entoptic  Observation  of  the  Vessels  of  the  Eetina  (Purkinje).  — 
a).  If,  in  a  dark  room,  we  hold  a  candle  at  some  distance  from  the  eye 
while  we  look  directly  in  front,  we  see  the  retinal  vessels  greatly 
magnified  projected  on  the  dark  portion  of  the  room.  They  appear 
dark  (of  a  deep  blue)  on  a  somewhat  more  luminous  ground  (orange).  — 
If  we  move  the  candle  towards  or  away  from  the  visual  line,  the  vessels 
seem  displaced  in  the  same  direction;  if,  on  the  contrary,  we  move  the 
candle  around  the  visual  line,  the  vessels  seem  to  move  in  the  direction 
opposite  to  that  of  the  candle.  The  fovea  appears  without  vessels:  in 
my  eye  it  offers  a  kind  of  starlike  appearance;  in  others  (Burow)  it 
appears  as  a  luminous  disc,  limited  by  a  crescent-shaped  shadow. 

The  explanation  of  these  phenomena  has  been  given  by  H.  Muller. 
By  refraction  there  is  formed  at  a  (fig.  105)  a  retinal  image  of  the  candle; 
the  part  of  the  retina  thus  illuminated  sends  diffuse  light  in  all  direc- 
tions. The  vessel  v  intercepts  the  rays  av,  so  as  to  form  the  shadow  b 
on  the  sensitive  layer  of  the  retina;  it  is  this  shadow  that  we  see  (the 
retina  is  represented  too  thick  on  the  figure ;  really  the  shadow  is  very 
near  the  vessel).  Illuminated  directly,  the  vessel  also  forms  a  shadow 


154  PHYSIOLOGIC   OPTICS 

on  the  sensitive  part  situated  behind  it ;  but  this  shadow  is  not  usually 
perceived,  because  it  is  always  formed  at  the  same  place  (and  because 
the  sensitive  layer  has  thus  become  accustomed  to  it)  or,  perhaps,  be- 
cause the  part  of  the  retina  which  is  behind  the  vessel,  being  always 
covered,  is  never  fatigued  and  consequently  remains  much  more  sensi- 
tive, so  that  the  little  light  which  passes  through  the  vessel  produces 
as  strong  an  impression  on  this  part  as  the  full  light  on  the  remainder 
of  the  retina. 


Fig.  105.  —  Entoptic  observation  of  the  vessels.    (After  H.  Muller.) 

It  seems  that  the  vessels  form  in  ordinary  circumstances  negative 
scotomata,  like  the  spot  of  Mariotte,  although  it  may  be  difficult  to  ob- 
serve them,  except  near  the  papilla,  because  of  the  instability  of  the 
fixation  (see  chap.  XVIII). 

b).  We  concentrate  with  a  convex  lens  the  light  of  a  flame  on  the 
sclera,  as  far  as  possible  from  the  border  of  the  cornea.  By  bringing 
the  focus  somewhat  on  the  sclera,  we  see  dark  vessels  on  an  orange 
ground.  The  vessels  move  in  the  same  direction  as  the  luminous  focus. 
On  concentrating  the  light  on  the  internal  part  of  the  sclera  we  succeed 
in  seeing  the  luminous  focus  itself  under  the  form  of  a  red  sun  near  the 
external  border  of  the  visual  field. 

The  explanation  is  analogous  to  that  of  the  preceding  case.  The 
light  of  the  image  of  the  flame,  formed  on  the  sclera,  passes  through  this 
membrane  and  the  choroid,  and  disperses  in  the  interior  of  the  eye 
where  it  forms  vascular  shadows  at  unusual  places.  —  H.  Midler  meas- 
ured the  distance  ab  (fig.  106),  separating  two  successive  positions  of 
the  luminous  focus,  and  the  displacement  «/5  of  the  shadow  of  a  vessel 
corresponding  to  this  displacement  of  the  light.  With  these  data,  he 
calculated  that  the  vessel  should  be  0.17  to  0.33  mm.  in  front  of  the 
sensitive  layer.  This  experiment  seems  to  prove  that  it  is  the  layer  of 


EXTOPTIC  PHENOMENA  155 

the  cones  and  rods  that  is  the  sensitive  layer,  for  the  distance  of  the 
small  vessels  near  the  macula  from  the  layer  with  the  cones  is  very 
nearly  the  same  (0.2  to  0.3  mm.). 

Another  phenomenon,  also  due  to  the  influence  of  the  light  which 
passes  through  the  sclera  and  the  choroid,  is  observed  when  we  place 
ourselves  near  the  luminous  source,  a  window  for  example,  so  that  one 
eye  may  be  illuminated  while  the  other  is  in  the  shade.  After  a  little 
while  we  then  observe,  on  closing  the  eyes  alternately,  that  the  white 
objects  seen  with  the  illuminated  eye  present  a  greenish  tint,  while  they 
appear  reddish  to  the  other  eye.  The  light  which  passes  through  the 
sclera  and  the  choroid  is  colored  red  by  the  blood  of  the  latter  mem- 
brane. This  red  light  "fatigues"  the  retina  of  the  illuminated  eye,  which 
has  the  effect  of  making  white  objects  assume  a  greenish  tint.  The 
other  eye  sees  them  red  by  contrast. 

When  we  read  in  full  sunlight,  we  sometimes  see  the  letters  vividly 
colored  red.  The  phenomenon  is  probably  of  the  same  kind  as  the 
preceding.  The  red  light,  which  passes  through  the  membranes  of  the 
eye,  comes  to  be  added  to  the  light  which  passes  through  the  pupil.  It 
is  not  sufficiently  great  to  perceptibly  change  the  tint  of  the  white 
paper,  brightly  illuminated  by  the  sun,  but  it  colors  red  the  black  letters, 
which  send  back  only  very  little  of  the  white  light. 

c).  Looking  at  the  sky  through  a  stenopaic  opening,  we  see  very  dis- 
tinctly pictured  the  granulated  ground  and  the  delicate  vessels  which 
surround  the  macula ;  but  the  stenopaic  opening 
must  be  kept  in  continuous  motion,  otherwise 
the  phenomenon  disappears.  If  we  look  at  the 
sky  without  the  stenopaic  opening,  the  shadow 
of  the  vessel  is  too  short  to  reach  the  sensitive 
layer.  The  same  phenomenon  is  frequently  ob- 
served when  working  with  the  microscope :  when 
we  illuminate  the  field  with  daylight,  we  see  the 
vessels  by  placing  the  eye  at  the  ocular  and  giv- 
ing it  a  to-and-fro  motion.  The  musca  of  the 

vitreous  body  may  also  be  very  well  observed    Fig.  106.  -  Entoptic  obser- 
vation of  the  vessels  by  il- 
m  this  way.  lumination  of  the  sclera. 

When  making  this  experiment,  as  well  as  the 

preceding  one,  we  sometimes  see  the  vessels  become  luminous ;  this  is 
due  to  the  fact  that  the  parts  of  the  sensitive  layer  on  which  the  shadow 
falls,  in  ordinary  circumstances,  are  now  exposed  to  the  light,  which 
acts  much  more  strongly  on  these  parts  than  on  the  remainder. 


150  ^ 

88.  Other  Entop tic  Phenomena.  —  a).  Looking  towards  the  sky.  \\  o  very 
frequently  see  bright  points  which  seem  to  move  lively  and  then  to 
disappear,  giving  place  to  others  (Pti/ v  ,  \  The  phenomenon  is  often 
more  pronounced  if  we  look  through  a  cobalt  glass.  This  phenomenon 
is  explained  by  the  pressure  which  is  exerted  on  the  sensitive  layer  by 
a  globule  of  blood  which  is  stopped  in  a  very  narrow  capillary,  (i) 

6),  By  compressing  the  eye  for  some  time,  we  can  see  the  retinal 
vessels  and  even  notice  the  blood  globules  magnified  about  50  times. 
The  retinal  vessels  appear  bluish;  but,  before  perceiving  them,  we  see 
those  of  the  chorio-capillary  membrane,  red  on  a  black  ground  (Vierordt, 
LaiWifi).  It  seems  that  this  experiment,  which  Young  had  already  made, 
would  not  succeed  with  everybody 

f).  A  pressure  localized  on  a  small  part  of  the  sclera  gives  rise  to  a 
pkosphcnc  which,  like  every  other  retinal  impression,  is  projected  in  the 
opposite  direction.  Making  the  experiment  in  darkness,  we  notice  that 
the  phosphene  has  the  form  of  a  feebly  luminous  disc,  surrounded  by 
a  bright  border,  corresponding  to  the  inflection  of  the  retina.  "With 
very  prominent  eyes  Young  succeeded  in  producing  a  phosphene  cor- 
responding to  the  macula:  exterior  objects  which  were  in  the  position 
of  the  phosphene  were  still  visible,  but  presented  very  pronounced  de- 
formities. —  If  we  exert  on  the  eye  a  pressure  sufficiently  strong 
uniform,  the  entire  visual  field  is  darkened  in  consequence  of  the  anemia 
of  the  retina. 

«0«  On  making,  in  a  dark  room,  rapid  movements  with  the  eyes,  we 
observe  two  luminous  circles  corresponding  to  the  places  of  entrance 
of  the  optic  nerves  and  due  to  the  traction  produced  by  these  nerves 
during  the  movement. 

e).  On  making  an  effort  of  accommodation  in  a  dark  room,  we  some- 
times see  a  very  large  luminous  circle,  which  is  attributed  to  the  trac- 
tion which  the  ciliary  muscle  exerts  on  the  interior  membranes  of  the 
eye  during  accommodation  (phosphene  of  accommodation  of  Csermak). 
I  did  not  succeed  with  this  experiment. 

/).  A  weak  electric  current  makes  visible  at  the  moment  of  clc 
the  dark  papilla  on  a  blue  ground,  if  the  current  is  ascending;  whitish 
blue  on  a  dark  orange  ground  if  the  current  is  descending:  on  opening 
the  current  we  have  the  phenomena  reversed.    If  the  current  is  strong, 
we  see  all  the  colors  of  the  spectrum  mixed. 


(1)  [Another  and  rery  probable  explanation  of  this  phenomenon  assumes  that  we  observe  in  the 
littJebritht  bom«  some  reiattT^y  empty  capillary  spaces,  produced  by  small  temporary  local  stoppages 
of  the  circulation  in  the  capillaries  of  the  retina.  See  the  paper  by  the  translator  in  the  QpAOotm* 
Jta*r<  February,  1900.]-  IT. 


BSTOPTIC  PBBSOMESJL  157 

g).  On  looking  towards  the  sky  through  a  Xicol  prism,  we  see  the 
brushes  of  Haidinger,  an  indistinct  cross,  one  of  the  arms  of  which  is 
yellow,  the  other  blue;  the  phenomenon  rotates  with  the  nicoL  Some 
persons  can  see  the  phenomenon,  but  less  pronounced,  without  a  nicoL 

A),  Phenomena  of  Diffraction*  in  the  Eye.  Looking  toward*  a  very  in- 
tensely luminous  point  we  see  it  surrounded  with  an  infinity  of  very 
fine,  many-colored  radiations,  the  whole  of  which  is  known  under  die 
name  of  ciliary  corona.  Its  extent  varies  with  the  intensity  of  the 
luminous  point.  If  the  latter  is  very  bright  (a  reflected  image  of  the 
sun)  the  diameter  of  the  corona,  may  reach  8  degrees  or  more.  The 
cause  of  the  phenomenon  is,  in  all  probability,  to  be  found  in  the  fibrous 
structure  of  the  crystalline  lens. 

Besides  the  ciliary  corona,  most  people  see  around  the  entire  luminous 
source  a  somewhat  vivid  diffraction  ring  A,  presenting  the  colors  in  the 
well-known  order:  red  outside,  brae  inside.  The  diameter  of  the  ring 
(blue)  is  about  3  degrees.  The  space  which  separates  it  from  the  lumin- 
ous source  is  filled  with  the  ciliary  corona. 

Druault  and  Solomonsohn  have  recently  described  a  second,  larger  ring 
B  (6  to  7  degrees  in  diameter),  winch  seems  to  appear  in  every  one  when 
the  pupil  is  dilated.  It  presents  the  colors  in  the  same  order  as  the  first, 
but  it  is  more  irregular,  and  composed  of  radial  striae.  Making  these 
observations  with  monochromatic  fight,  the  ciliary  corona,  presents  itself 
under  the  form  of  a  luminous  dust,  which  is  concentrated  towards  the 
periphery  so  as  to  form  the  two  rings  which  I  have  just  described. 
Quite  near  the  luminous  source  we  see  one  or  two  black,  very  fine 
rings,  due  to  diffraction  by  the  border  of  the  pupiL 

The  ring  A  is  probably  due  to  the  epithelial  cells  of  the  cornea,  and 
analogous  to  the  rings  which  we  observe  on  looking  through  a  glass 
plate  covered  with  grains  of  lycopodium.  On  covering  a  larger  and  larger 
part  of  the  pupil  with  a  screen,  we  see  the  entire  ring  become  indistinct 
and  disappear  at  once.  Schioetz  has  shown  that  on  exposing  the  cornea, 
to  the  action  of  distilled  water  for  some  time,  as  in  the  experiment  of 
Young,  page  168,  we  observe  a  pretty  system  of  rings,  the  first  of 
which  corresponds  almost  to  the  ring  A.  We  must  note,  however,  that 
Druavlt,  on  looking  through  a  dead  cornea,  showed  the  existence  of  a 
ring,  the  dimensions  of  which  scarcely  differed  from  those  of  the  ring  A, 
and  which  was  undoubtedly  due  to  the  endothelium  of  the  membrane  of 
Descemet:  he  could  remove  the  entire  epithelium  of  the  anterior  surface 
without  producing  the  least  change  in  the  ring,  which  would,  on  the 
contrary,  disappear  as  soon  as  he  touched  the  endothelium. 


158  PHYSIOLOGIC  OPTICS 

The  ring  B,  which  was  previously  described  by  Danders,  is  due  to  the 
crystalline  fibres  which  act  as  a  grating.  If  we  cover  a  part  of  the  pupil 
with  a  screen,  we  see  a  part  of  the  ring  disappear  while  the  remainder 
does  not  change.  Druault  succeeded  in  reproducing  the  phenomenon 
with  dead  crystalline  lenses. 

The  rings  which  glaucomatous  patients  see  resemble  these  rings,  but 
are  generally  larger  (10  to  n  degrees).  As  the  size  of  the  rings  is  in- 
versely proportional  to  that  of  the  corpuscles  which  produce  them,  it 
is  probable  that  the  origin  of  the  glaucomatous  rings  is  to  be  found  in 
the  deepest  layer  of  the  corneal  epithelium,  the  cells  of  which  are  much 
smaller  than  the  superficial  cells  (Schioetz).  Placing  a  drop  of  blood  in 
the  conjunctival  sac  we  obtain  a  very  pretty  ring  (diameter  7.5  degrees 
for  the  yellow)  surrounded  by  a  second  paler  ring.  The  space  between 
the  first  ring  and  the  light  is  not  black,  as  for  the  other  rings  here  de- 
scribed, but  yellowish  or  maroon  (Druault).  These  rings  seem  analogous 
to  those  sometimes  seen  by  persons  affected  with  conjunctivitis. 

i).  I  recently  described  a  kind  of  entoptic  phenomenon  which  I  ob- 
served in  the  following  circumstances.  We  surround  a  lamp  with  a 
transparent  shade,  made  of  some  layers  of  colored  tissue  paper,  for  ex- 
ample. We  place  ourselves  at  some  meters  distance,  and  interpose  an 
opaque  screen,  in  which  has  been  cut  a  vertical  slit,  between  the  lamp 
and  the  eye ;  the  distance  of  the  screen  from  the  eye  may  vary  between 
30  cm.  and  several  meters.  We  close  the  left  eye  and  fix  with  the  right 


Fig.  106a.  —  Entoptic  phenomenon. 

eye  a  point  on  the  screen,  situated  near  the  right  border  of  the  slit. 
To  begin,  we  hold  the  head  so  that  the  eye  may  be  in  darkness.  Then 
we  move  the  head  so  that  the  eye  enters  into  the  luminous  pencil  which 
passes  through  the  slit  while  maintaining  fixation  at  the  same  place. 


ENTOPTIC  PHENOMENA  159 

At  the  same  moment  we  see  the  phenomenon  appear  under  the  form 
of  two  blue  arcs,  feebly  luminous,  but  bright,  which  go  from  the  slit 
towards  the  position  of  the  blind  spot  by  turning  around  a  fixed  point 
(fig.  1060).  The  phenomenon  lasts  only  a  moment;  an  instant  later  the 
arcs  become  narrow,  the  interior  which  was  black  is  filled  with  a  blue 
glow,  and  the  whole  disappears,  to  reappear  again  with  the  least  motion 
of  the  eye.  To  see  the  phenomenon  with  the  left  eye  it  is  necessary  to 
fix  the  left  border  of  the  slit. 

According  to  a  communication  from  Dr.  Crzellitzer  the  phenomenon 
was  described  by  Purkinje  in  a  publication  which  I  have  not  at  my  dis- 
posal. It  seems  very  prevalent ;  among  persons  whom  I  have  examined 
in  this  regard,  I  have  met  only  a  single  one  who  has  not  been  able  to  see 
it.  The  form  of  the  arcs  recalls  the  course  of  the  nerve  fibres  at  this 
place.  The  appearance  resembles  that  of  certain  phosphorescent  bodies, 
by  the  bluish  color  and  by  the  impression  which  it  gives  of  being  feeble 
and  yet  bright  at  the  same  time ;  we  again  find  the  same  appearance  for 
different  other  phenomena  which  we  observe  in  darkness,  for  instance 
the  after  image  of  Purkinje  (see  page  242),  the  trace  which  the  im- 
pression of  a  red  coal  leaves  on  the  retina,  and  so  forth. 

Bibliography.  —  (Euires  de  Young,  edited  by  Tscherning,  p.  71, 140  and  168.  —  Purkinje 
(J.  E.).  Beitrdge  zvr  Kentniss  des  Sehens,  1819,  p.  89,  et  neue  Beitrdge,  1825,  p.  115.  —  List- 
ing (J.).  Beitrag  zur  physiologischen  Optik.  Gb'ttingen,  1845.  —  Doncan  (A.).  De  corporis 
vitrei  structurd.  Utrecht,  1854.  —  Brewster  (D.).  Transactions  of  the  Royal  Soc.  of  Edinb., 
XV,  377.  —  Miiller  (Heinrich).  Verh.  der  med.  physik.  Gesdlschaft  zu  Wurzburg.  IV,  V.  — 
Haidinger.  Ueber  das  directs  Erkennen  des  polarisirten  Lichts  und  der  Lage  der  Polarisations- 
ebene.  Poggend.  Ann.  1844.  —  Darier  (A.).  De  la  possibilite  de  voir  son  propre  cristallin  Ann. 
d'oc.  t.  CXIV,  p.  198,  1895.  —  Schioetz  (H.).  Om  nogle  optiske  equeskaber  ved  Cornea. 
Christiana,  1882.  —  Druault  (A.).  Sur  la  production  des  anneaux  colores  autour  des  flammes. 
Arch,  d'ophtalmol,  Mai,  1898,  et  Compte  rendu  du  Congres  <f  Utrecht,  1899.  —  Salomonsohn 
(H.).  Ueber  Lichtbeugung  an  Hornhaut  und  Linse.  Arch.f.  Anal.  u.  Phys.,  1898.  Tscherning 
(M.)  Eine  Selbstbeobachtung.  XL  M.  f.  A.  June,  1898.  —  Tscherning  (M.).  Compte  rendu 
du  Congres  a'  Utrecht,  1899. 


CHAPTER  XII. 

ACCOMMODATION. 


83.  Measurement  of  the  Amplitude  of  Accommodation.  —  We  have  de- 
fined the  amplitude  of  accommodation  as  the  difference  between  the 
distances  of  the  far  point  and  the  near  point,  measured  in  dioptrics.  It 
expresses  the  value  of  a  convex  lens  which,  added  to  the  eye,  would 
form  an  image  of  the  near  point  at  the  position  of  the  far  point. 

For  the  determination  of  the  near  point  it  is  necessary,  on  account  of 
the  relation  between  accommodation  and  convergence,  which  I  shall 
discuss  later,  to  close  the  eye  which  we  are  not  examining.  In  order 
to  reach  the  highest  degrees  of  accommodation,  the  patient  is  some- 
times obliged  to  squint  inwards,  and,  if  both  eyes  are  open,  the  need  of 
seeing  single  will  prevent  him  from  attaining  the  limit  of  his  accommo- 
dation. In  clinics,  we  generally  confine  ourselves  to  determining  the 
shortest  distance  at  which  the  patient  can  read  fine  print.  It  is  neces- 
sary, for  this  determination,  to  use  very  small  letters,  otherwise  the 
patient  may  still  read  them  within  the  near  point,  although  seeing  the 
letters  only  indistinctly.  —  Another  method  consists  in  determining  the 
strongest  concave  glass  through  which  the  patient  can  see  distant  ob- 
jects distinctly  (the  table  of  visual  acuity),  since  the  concave  glass  forms 
an  image  of  them  so  much  nearer  in  proportion  as  it  is  stronger.  We 
can  also  use  optometers,  that  of  Badal  or  of  George  Bull  (i)  for  example. 

The  determination  of  the  near  point  is  always  uncertain,  because  we 
can  never  know  whether  the  patient  makes  a  maximum  effort  or  not. 
It  succeeds  especially  poorly  in  persons  of  little  intelligence,  in  children, 
etc.  Anyhow,  to  determine  it  exactly  is  generally  of  little  practical  im- 
portance ;  if  we  desire  an  exact  measurement,  we  can  instil  eserine,  but 
we  thus  obtain  an  amplitude  slightly  higher  than  that  which  the  patient 
would  attain,  even  when  trying  his  best. 


(1)  The  optometer  of  Bull  resembles  externally  that  of  Young,  enlarged,  but  the  principle  is  differ- 
ent. We  look  through  a  lens  of  6  D.  without  slits,  and  the  line  is  replaced  by  a  series  of  small  dominoes. 
The  patient  must  simply  tell  the  most  distant  and  nearest  of  these  dominoes  that  he  can  see  distinctly. 

160 


ACCOMMODATION  161 

For  scientific  researches  it  may  sometimes  be  important  to  know 
exactly  the  amplitude  of  accommodation.  We  can  then  determine  it 
with  the  optometer  of  Young,  if  the  observer  is  master  of  his  accom- 
modation, that  is  to  say,  if  he  can  make  an  effort  of  accommodation 
without  fixing  a  near  object.  If  not,  the  best  means  is  to  offer  a  hair 
in  a  ring,  and  to  see  how  close  we  can  move  it  to  the  eye  before  it 
appears  dim.  We  may  with  advantage  add  this  ring  to  the  optometer 
of  Young. 

The  amplitude  of  accommodation  diminishes  in  a  very  regular  manner 
with  age.  According  to  Danders,  the  diminution  begins  to  make  itself 
felt  at  the  close  of  infancy.  It  is  so  regular,  at  least  beginning  at  25  or 
30  years,  that  we  can  frequently  determine  the  age  of  the  patient  to 
almost  within  one  or  two  years,  by  means  of  the  optometer  of  Bull,  for 
example.  At  the  age  of  47  or  48  years  this  diminution  begins  to  manifest 
itself  in  emmetropes,  by  the  appearance  of  presbyopia.  In  hypermetropes 
the  presbyopia  makes  its  appearance  sooner;  it  appears  later  in  low 
myopia,  and  myopes  of  a  high  degree  never  become  presbyopic,  although 
the  amplitude  of  accommodation  diminishes  in  them  as  in  every  one  else. 
In  emmetropes  it  is  very  rare  to  find  an  exception  to  the  rule  laid  down 
above,  unless  the  pupil  is  very  small.  If,  therefore,  a  patient  reads 
without  glasses  when  over  50  or  55  years  old,  he  must  be  myopic,  if 
the  pupil  is  of  the  ordinary  size. 

Presbyopes  do  not  suffer  from  accommodative  asthenopia ;  when  read- 
ing they  are  obliged  to  hold  the  book  farther  away,  especially  in  the 
evening;  the  manner  in  which  they  hold  the  book,  far  from  their  eyes 
*and  near  the  lamp,  is  very  characteristic. 

As  to  the  choice  of  spectacles,  it  is  clear  that  if  we  fix  on  a  distance 
for  work  of  33  centimeters  we  are  never  obliged  to  give  to  an  emme- 
trope  glasses  of  a  greater  strength  than  3  dioptrics.  But  it  is  frequently 
useful,  especially  when  the  acuity  is  diminished,  to  choose  a  shorter 
distance  for  work,  for  example  25  centimeters,  corresponding  to  4 
dioptrics.  We  frequently  notice  a  tendency  to  give  somewhat  stronger 
glasses,  which,  however,  cause  only  slight  inconvenience.  Thus,  the 
series 

50  55  60  65  years 

-f-1  +2  +3  +4  dioptrics 

is,  perhaps,  a  little  strong,  especially  for  high  degrees. 

PARALYSIS  OF  ACCOMMODATION.  —  We  meet  this  disease  especially 
in  children  who  have  had  diphtheria.  If  we  learn  that  the  child  has  not 
been  able  to  read  for  some  time  past,  although  it  sees  perfectly  at  a 


1G2  PEJSIOLOGIC   OPTICS 

distance,  and  if  we  do  not  find  hypermetropia,  we  may  be  almost  certain 
that  it  has  had  diphtheria.  The  diagnosis  of  paralysis  is  verified  when 
the  child  reads  well  with  the  proper  convex  glasses.  Generally  there 
are  no  other  symptoms  of  ocular  paralysis,  among  others  no  mydriasis. 
We  prescribe  convex  glasses  almost  until  the  recovery,  which  generally 
takes  place  in  a  space  of  two  or  three  months. 

The  second  form  of  paralysis  which  we  occasionally  meet  is  that  which 
forms  part  of  a  more  or  less  complete  paralysis  of  the  third  pair.  It  is 
usually  accompanied  by  mydriasis  and  frequently  by  paralysis  of  ex- 
ternal muscles.  It  seems,  however,  that  it  may  exist  without  any  com- 
plication. —  In  glaucoma  and  cyclitis,  the  diminution  of  the  amplitude 
of  accommodation  is  frequently  one  of  the  first  symptoms. 

SPASM  OF  ACCOMMODATION.  —  There  have  been  described  two  forms 
of  spasm  of  accommodation.  i°  As  we  have  seen,  one  has  been  accus- 
tomed to  diagnose  spasm  of  accommodation  when  one  found  a  weaker 
refraction  after  the  instillation  of  atropine.  The  existence  of  this  sup- 
posed spasm,  which  is  always  of  a  very  low  degree  (0.50  to  1.50  D.),  is 
very  doubtful,  since  the  diminution  of  refraction,  after  the  instillation 
of  atropine,  may  often  be  attributed  to  the  weaker  refraction  of  the 
peripheral  parts  of  the  optic  system  of  the  eye. 

2°  We  sometimes  observe  in  hysterical  patients  a  true  spasm  of  ac- 
commodation, extending  most  frequently  to  the  entire  amplitude,  and 
not  to  a  small  part,  as  in  the  preceding  case.  These  cases  are  rare;  they 
give  rise  to  a  transient  myopia,  which  is  generally  complicated  by 
monocular  diplopia. 

84.  Mechanism  of  the  Accommodation.  Historical,  A.  —  Theoretically, 
the  eye  could  accommodate  itself  by  one  of  the  following  mechanisms : 

a.  INCREASE  OF  CURVATURE  OF  THE  CORNEA. 

b.  INCREASE  OF  CURVATURE  OF  THE  CRYSTALLINE  LENS. 

c.  ELONGATION  OF  THE  GLOBE. 

These  three  hypotheses  have  found  their  adherents,  as  also  have  the 
two  following  which  are  theoretically  impossible : 

d.  ADVANCE  OF  THE  CRYSTALLINE  LENS. 

e.  CONTRACTION  OF  THE  PUPIL. 

As  to  the  hypothesis  d,  we  must  note  that,  even  if  the  crystalline  lens 
would  advance  so  as  to  touch  the  cornea,  this  advance  would  not  suffice 
to  explain  any  considerable  amplitude  of  accommodation.  —  The  accom- 
modative contraction  of  the  pupil  was  discovered  by  Schemer.  By  look- 
ing through  an  opening  a  little  smaller  than  the  pupil,  it  is  easy  to  con- 


9 

ACCOMMODATION  163 

vince  one's  self  that  this  contraction  is  not  sufficient  to  explain  accom- 
modation. 

Apart  from  these  five  theories,  there  have  been  proposed  still  others, 
much  less  plausible.  Kepler,  who  was  the  first  to  propound  the  problem 
of  the  mechanism  of  accommodation,  supposed  an  advance  of  the  crys- 
talline lens,  whilst  Descartes  was  the  first  to  suppose  an  increase  of 
curvature  of  this  organ. 

The  theory  of  the  change  of  curvature  of  the  cornea  found  support  in 
the  measurements  of  this  curvature  made  by  Home  and  Ramsden  towards 
the  end  of  the  last  century.  —  The  discussion  continued  until  towards 
the  middle  of  the  century,  and  the  false  hypotheses  on  the  nature  of 
accommodation  have  even  resulted  in  two  beautiful  discoveries.  The 
theoretical  researches  of  Sturm  on  the  form  of  the  astigmatic  pencil 
were,  indeed,  undertaken  to  prove  that  accommodation  did  not  exist: 
this  author  thought  that  distant  objects  were  seen  with  the  posterior 
part  and  near  objects  with  the  anterior  part  of  the  focal  interval.  On  the 
other  hand,  when  Arlt  discovered  that  myopia  depended  on  the  elonga- 
tion of  the  globe,  he  was  guided  by  a  false  idea  on  accommodation.  He 
thought  that  the  action  of  the  external  muscles  produced  an  elongation 
of  the  globe,  when  one  is  forced  to  see  close  at  hand;  and,  as  it  was 
known  that  myopia  was  a  consequence  of  near  work,  he  concluded  that 
myopia  must  be  produced  by  an  elongation  of  the  globe.  On  making 
an  autopsy  on  some  excessively  myopic  eyes,  he  proved  the  lengthening 
of  the  globe  in  these  cases,  and  believed  that  he  had  thus  confirmed  his 
hypothesis.  We  now  know  that  this  form  of  myopia  does  not  depend 
on  near  work,  and  that  accommodation  is  not  obtained  by  an  elongation 
of  the  globe,  but  by  an  increase  of  curvature  of  the  crystalline  lens ! 

The  question  was  decided  by  the  observation  of  the  changes  of  the 
images  of  Purkinje  during  accommodation,  which  prove  that  accom- 
modation is  effected  by  an  increase  of  curvature  of  the  anterior  surface 
of  the  crystalline  lens.  The  discovery  was  made  in  1849  by  Max  Langcn- 
beck,  but  attracted  scarcely  any  attention ;  it  was  only  after  the  beautiful 
researches  of  Cramer  (1851-52)  that  the  truth  was  definitely  accepted. 
Cramer  constructed  an  instrument  which  he  called  ophthalmoscope,  with 
which  he  could  conveniently  observe  the  catoptric  images  of  the  crystal- 
line lens,  and  it  was  easy  for  him  to  show  that  that  of  the  anterior  surface 
made,  during  accommodation,  a  quite  extended  centripetal  movement. 
This  fact  has  been  verified  by  all  those  who  have  examined  the  catoptric 
images  during  accommodation ;  it  is  due  to  the  increase  of  curvature 
of  the  anterior  surface. 


164 


PHYSIOLOGIC   OPTICS 


Let  ABD  (fig.  107)  be  the  surface  in  a  state  of  repose  and  C  its  center, 
AjBDi  the  surface  in  a  state  of  accommodation  and  Ct  its  center,  O  an 
object  (a  lamp  placed  at  a  great  distance).  To  find  the  position  of  the 
image,  we  draw  OC  (OQ)  (supposing  that  these  are  the  apparent  sur- 
faces we  need  not  take  into  account  the  corneal  refraction).  The  image 
must  be  on  this  straight  line,  at  an  equal  distance  between  the  surface 
and  center,  at  I  for  the  surface  in  repose,  at  Ij_  for  the  surface  in  a  state 


Eh 


Fig.  107.  —  Centripetal  movement  of  the  catoptric  image  of  the  anterior  surface  of  the 
crystalline  lens  during  accommodation.     (Discovered  by  Cramer.) 


of  accommodation.  The  observing  eye  sees  the  images  projected  in  the 
pupillary  plane,  it  sees  I  at  i  and  I±  at  ^ ;  it  sees  the  image,  therefore, 
make  a  centripetal  movement  during  accommodation.  It  is  the  same, 
whatever  may  be  the  position  of  the  observing  eye;  there  is  only  one 
point  where  it  does  not  see  motion,  viz.,  when  it  is  on  the  prolongation 
of  line  II^  in  this  case  the  two  images  I  and  I±  overlap,  and  there 
is  no  apparent  displacement.  The  line  II±  passes  through  the  point  B, 
the  place  where  the  two  surfaces  touch.  This  point  B,  towards  which 
the  apparent  movement  of  the  image  takes  place,  whatever  may  be  its 
position  in  the  pupil,  is  usually  situated  a  little  outside  the  center  of  the 
latter;  generally  it  is  found  almost  on  the  optic  axis  of  the  eye.  — 
Recently,  Coronat  again  described  the  centripetal  movement,  whence  he 
erroneously  inferred  a  see-saw  movement  of  the  crystalline  lens. 

The  question  of  knowing  by  what  change  the  eye  accommodates  itself 
for  near  vision  being  solved,  it  remained  to  be  discovered  by  what  means 
the  change  was  effected.  Cramer  attributed  the  change  to  the  contrac- 
tion of  the  iris ;  he  thought  that  the  iris  in  the  state  of  repose  was  greatly 
swollen  in  front,  and  became  flattened  during  accommodation  by  a 
simultaneous  contraction  of  the  sphincter  and  dilatator.  He  thought  that 


ACCOMMODATION  165 

it  thus  exerted  a  pressure  on  the  peripheral  parts  of  the  crystalline  lens, 
and  that  the  ciliary  muscle,  contracting  at  the  same  time,  exerted  a 
traction  on  the  choroid,  which  pushed  the  vitreous  body  forward.  In 
this  way  the  crystalline  lens,  subjected  to  a  pressure  in  its  whole  extent, 
except  on  the  pupillary  part,  became  swollen  at  this  place.  Several  other 
theories,  conceived  after  that  of  Cramer,  also  involved  the  participation 
of  the  iris  in  the  act  of  accommodation ;  they  were  necessarily  abandoned 
when  Graefe  published  his  celebrated  case  of  complete  aniridia,  of 
traumatic  origin,  in  which  the  amplitude  of  accommodation  was  intact. 

A  short  time  after  the  discovery  of  Cramer,  and  without  being  ac- 
quainted with  his  work,  which  was  published  only  in  the  Dutch  language, 
Hclmholtz  made  the  same  observation.  He  used  as  his  object  the  dis- 
tance between  two  lamps  (or  a  lamp  and  its  image  formed  by  a  mirror). 
During  accommodation,  the  distance  between  the  two  images  diminished 
considerably,  which  is  easy  to  understand,  since  a  sphere  forms  an  image 
smaller  in  proportion  as  its  radius  is  less. 

Hclmholtz  confirmed,  moreover,  the  observation  made  previously  by 
Hueck,  according  to  which  the  anterior  surface  of  the  crystalline  lens 
advances  a  little  during  accommodation.  He  measured  the  thickness 
of  the  crystalline  lens,  which  he  found  a  little  greater  during  accommo- 
dation than  in  a  state  of  repose.  He  also  measured  two  dead  crystalline 
lenses,  and  found  their  thickness  greater  than  that  of  the  living  crystal- 
line lens  in  a  state  of  repose.  He  further  concluded  that  there  was  a 
slight  increase  of  curvature  of  the  posterior  surface  of  the  crystalline 
lens  during  accommodation. 

The  following  are  the  numbers  which  he  adopted  for  his  schematic 
eye,  compared  with  those  which  he  found  for  the  dead  eye : 

SCHEMATIC  EYE  DEAD  EYE 

Repose.    Accommodation.  A  B 

Kadiusof  the  anterior  surface..       10mm               6ram  10.16mm  8.87mm 

—        —     posterior  surface .         6mm               5.5mm  5.86mm  5.89mm 

Thickness 3.6mm            4mm  4.2mm  431mm 

Focal  distance 43.71mm        33.79Bim  45.14mn>  47.44mm 

Total  index 1.4545  1.4519         1.4414 

Later,  he  supposed  for  the  schematic  eye  an  index  of  1.4371,  which 
would  give  for  the  living  eye  in  repose  a  focal  distance  of  50.62  mm. 
and  for  the  eye  in  accommodation  39.07  mm. 

To  explain  the  mechanism  of  accommodation  Helmholtz  announced 
the  following  hypothesis,  which  he  gave,  however,  only  as  probable:  in 
a  state  of  repose  the  crystalline  lens  is  kept  flattened  by  a  traction 
exerted  by  the  zonula.  When  the  ciliary  muscle,  of  which  he  considered 


166  PHYSIOLOGIC  OPTICS 

the  anterior  extremity  as  fixed,  contracts,  it  draws  the  choroid  slightly 
forward,  which  relaxes  the  zonula.  Having  become  free,  the  crystalline 
lens  then  swells  by  its  own  elasticity,  approaching  the  spherical  form. 

This  hypothesis  does  not  seem  to  have  been  at  first  generally  ac- 
cepted, (i)  Hencke,  and  other  authors,  tried  to  explain  the  phenomena 
observed  by  other  hypotheses.  After  having  discovered  the  supposed 
circular  fibres  of  the  ciliary  muscle,  H.  Mulkr  thought  that  this  muscle 
changed  the  form  of  the  crystalline  lens  by  a  direct  pressure,  an  idea 
which  was  abandoned  when  it  became  known  that  the  ciliary  body  never 
touches  the  crystalline  lens. 

On  the  other  hand,  the  hypothesis  of  Helmholts  was  strengthened  by 
the  experiments  which  Hensen  and  Voelkers  performed  on  dogs.  They 
thrust  very  fine  needles  into  the  eye  a  little  behind  the  ora  serrata ;  on 
stimulating  by  the  electric  current  the  ciliary  ganglion,  they  saw  the 
free  extremity  of  the  needle  describe  a  movement  backwards,  which 
proves  that  the  choroid  is  drawn  forwards.  The  phosphene  of  Czermak, 
which  had  also  been  seen  by  Purkinje,  also  indicates  a  traction  forwards 
of  the  interior  membranes  of  the  eye.  By  examining  eyes  on  which  an 
iridectomy  had  been  performed,  Coccius  also  established  during  accom- 
modation, phenomena  which  could  militate  in  favor  of  the  hypothesis  of 
Helmholts  (swelling  of  the  ciliary  processes,  at  least  apparent  diminution 
of  the  diameter  of  the  crystalline  lens,  and  an  increase  in  the  width  of  its 
border,  that  is  to  say,  of  the  very  peripheral  part  which  is  seen  black  with 
the  ophthalmoscope). 

Thanks  to  these  observations,  thanks  also  to  the  ever  increasing  fame 
of  Helmholts,  his  theory  ceased  little  by  little  to  be  disputed,  and  his 
followers,  more  loyal  than  the  king,  proclaimed  as  certain  what  he  had 
himself,  with  much  reserve  explained  as  probable.  (2)  Thus,  Mauthner 
declared  the  question  of  accommodation  definitely  solved  by  the  theory 
of  Helmholts. 

Before  explaining  the  mechanism  of  accommodation  as  I  intend  to, 
I  must  add  some  remarks  to  the  historical  explanation  which  we  have 

(1)  See  Bonders.  Anomalies  of  the  Refraction  of  the  Eye.  London,  1864. 

(2)  Great  men  are,  indeed,  too  reserved  through  fear  of  their  followers.    HelmhoUz  formed  the  idea 
of  comparing  the  cornea  to  an  ellipsoid,  and  although  he  said  intentionally  that  the  cornea  does  not 
resemble  such  a  surface,  this  idea  has  so  taken  root  that  it  will  be  difficult  to  eradicate  it.    It  is  so  also 
with  his  ideas  of  accommodation ;  if  we  take  the  trouble  to  compare  the  cautious  terms  which  he  used, 
Avith  the  mode  of  expression  of  his  followers,  we  shall  see  the  difference.  The  participation  of  the  pos- 
terior iurface  of  the  crystalline  lens  in  accommodation,  which  everybody  considers  as  certain,  had  for 
Helmhottz  merely  the  character  of  a  grand  probability.  —  Measuring  his  three  living  eyes,  he  found  for 
the  crystalline  lens  a  thickness  about  %mm.  less  than  that  of  dead  crystalline  lenses ;  and  he  added  : 
"  On  the  other  hand,  it  seems  to  me  very  improbable  that  I  have  committed  an  error  of  a%mm.  mak- 
ing these  measurements."  In  the  modern  treatises  we  read,  on  the  contrary :  "  If  we  remove  the  crys- 
talline lens  of  the  eye  of  a  young  person,  AVC  see  it  immediately  assume  a  spherical  form,"  etc. 


ACCOMMODATION  167 

just  read,  and  which  is  classical,  because  there  have  been  authors  who 
have  expressed  ideas  on  accommodation  in  my  opinion  more  correct 
than  those  in  vogue  up  to  the  present  time.  First,  I  will  make  an  objec- 
tion. If  it  is  true  that  the  crystalline  lens,  in  repose,  is  kept  flattened 
by  a  traction  exerted  by  the  zonula,  we  should  expect  to  find  the  dead 
crystalline  lens,  taken  from  the  eye  in  its  capsule,  in  a  state  of  maximum 
accommodation,  or  perhaps  even  still  more  swollen,  since  it  is  no  longer 
exposed  to  any  traction.  The  followers  of  Helmholtz  have,  indeed, 
strongly  insisted  on  the  fact  that  he  found  the  dead  crystalline  lens 
thicker  than  the  living  crystalline  lens  in  repose,  although  the  difference 
does  not  seem  to  exceed  the  limit  of  error  (see  page  71) ;  but,  if  we 
take  the  trouble  of  examining  his  numbers  (page  165),  we  shall  see  that 
his  dead  crystalline  lenses  were  by  no  means  in  a  state  of  accommoda- 
tion. He  measured  in  all  three  living  eyes  and  found,  as  radii  of  the 
anterior  surface  of  the  crystalline  lens  in  repose,  11.9  mm.,  8.8  mm.  and 
10.4  mm.,  while  for  the  dead  eyes  he  found  10.16  mm.  and  8.87  mm. 
His  autopsies,  therefore,  by  no  means  tell  in  favor  of  his  hypothesis. 

It  is  so  also  in  the  case  of  the  measurements  which  Stadfeldt  under- 
took recently.  He  measured  eleven  living  human  crystalline  lenses  in 
a  state  of  repose,  with  the  ophthalmometer ;  the  radius  of  curvature  of 
the  anterior  surface  of  the  crystalline  was  on  an  average  10.6  mm.,  while 
the  average  of  the  same  radius  of  the  six  dead  crystalline  lenses,  taken 
from  the  eye  in  the  capsule  and  measured  with  the  ophthalmometer  of 
Javal,  without  being  exposed  to  any  traction,  was  11.4  mm. 

85.  Jttechanism  of  Accommodation.  Historical,  B.  —  It  was  Young  who 
first  demonstrated  that  accommodation  was  effected  by  an  increase  of 
curvature  of  the  crystalline  surfaces.  Moreover,  he  had  more  exact 
ideas  on  what  happened  during  accommodation  than  those  which  are 
actually  now  in  vogue.  He  wrote  his  celebrated  treatise  on  the  mechanism 
of  the  eye  in  1801,  and  it  is  truly  astonishing  that  nearly  a  century  should 
have  passed  before  his  book  was  understood  and  before  we  came  to 
know  as  much  as  he.  Before  proving  that  the  accommodation  is  effected 
by  an  increase  of  curvature  of  the  crystalline  lens,  he  begins  by  showing 
that  there  can  be  question  only  about  an  increase  of  curvature,  either 
of  the  cornea  or  of  the  crystalline  lens,  or  of  a  lengthening  of  the  globe, 
and  he  eliminates,  as  theoretically  impossible,  the  other  hypotheses 
which  had  been  proposed.  —  Let  us  now  pass  to  his  analysis. 

a.  ACCOMMODATION  is  NOT  EFFECTED  BY  AN  INCREASE  OF  CURVATURE 
OF  THE  CORNEA.  —  Young  proved  this  thesis  by  a  series  of  experiments, 


168 


PHYSIOLOGIC  OPTICS 


Young.) 


several  of  which  closely  approach  our  modern  ophthalmometric 
methods.  Observing  the  corneal  image,  he  did  not  discover  the  least 
change  during  accommodation;  he  obtained,  however,  a  very  visible 
change  by  exerting  a  pressure  on  a  peripheral  part  of  the  cornea,  and 
this  change  of  curvature  is  much  less  considerable  than  that  which 

would  be  necessary  to  explain  accommoda- 
tion. 

It  is  evident  that  a  change  of  the  cornea 
sufficient  to  explain  accommodation  would 
have  been  very  visible.  Young,  who  experi- 
mented with  his  own  eyes,  was  at  this  time  27 
years  old,  and  his  amplitude  of  accommoda- 
tion measured  about  10  D.  Actually,  we  can 
easily  measure  a  quarter  of  a  dioptry. 

His  most  conclusive  experiment  consisted 

in  Puttin?  the  e>'e  Under  Water  <fi*  Io8):  he 
took  a  weak  objective  of  a  microscope  which 

had  very  nearly  the  same  refraction  as  the  cornea,  filled  the  tube  with 
water,  and  placed  it  before  his  eye  also  plunged  into  water.  In  these  con- 
ditions, the  action  of  the  cornea,  which  was  surrounded  by  the  liquid  on 
both  sides,  was  eliminated  and  replaced  by  that  of  the  objective.  Now 
in  this  experiment  the  amplitude  of  the  accommodation  remained  intact. 

b.  ACCOMMODATION  is  NOT  EFFECTED  BY  AN  ELONGATION  OF  THE 
GLOBE.  —  To  prove  this  fact  Young  employed  a  method  which  he  could 
use  because  he  had  very  prominent  eyes.     He  turned  the  eye  inwards 
as  much  as  he  could,  and  applied  against  its  anterior  surface  a  strong 
iron  ring;  then  he  thrust  the  ring  of  a  little  key  on  the  external  side 
between  the  eye  and  the  bone,  until  the  phosphene  reached  the  fovea. 
The  rings  were  kept  at  a  fixed  distance.    Placed  between  the  iron  ring 
and  that  of  the  key,  the  eye  could  not  lengthen.    He  should  therefore, 
if  accommodation  was  effected  by  a  lengthening  of  the  globe,  either 
find  it  abolished,  or  see  in  every  case  the  phosphene,  due  to  the  pressure, 
extend  over  a  much  greater  surface.    But  in  these  conditions  the  accom- 
modation remained  unaltered,  and  the  width  of  the  phosphene  did  not 
change. 

c.  PERSONS  OPERATED  ON  FOR  CATARACT  HAVE  LOST  ALL  TRACE  OF 
ACCOMMODATION.  —  By  measuring  with  his  optometer  persons  operated 
on  for  cataract,  Young  easily  succeeded  in  proving  this  fact. 

d.  He  then  explained  the  direct  proofs  of  the  increase  of  curvature  of 
the  crystalline  lens.    It  was  to  these  experiments  that  I  alluded  when  I 


ACCOMMODATION 


169 


said  that  he  had,  on  accommodation,  ideas  which  are  ahead  of  our  own 
time.  I  again  performed  these  experiments  some  years  ago,  and  it  was 
by  starting  from  them,  by  repeating  them  and  adding  others  to  them, 
that  on  the  mechanism  of  accommodation  I  have  come  to  form  ideas 
which  differ  materially  from  those  which  have  been  current  up  to  the 
present. 

It  was  impossible  for  Voting  to  describe  clearly  the  mechanism  of 
accommodation,  because  at  that  time  the  non-striped  muscle  fibres  were 
unknown,  which  kept  him  from  suspecting  the  contractility  of  the  body 
known  later  as  the  ciliary  muscle ;  he  was  thus  led  to  postulate  the  con- 
tractility of  the  crystalline  lens,  an  hypothesis  which  he  soon  abandoned. 
His  researches  in  this  direction  necessarily  could  not  but  remain  fruit- 
less. 

The  ciliary  muscle  was  discovered,  at  the  same  time  and  separately, 
by  Bowman  and  Bruecke  (in  1846).  Ideas  on  the  structure  and  function 
of  this  muscle  have  varied  considerably.  Sometimes  the  anterior  ex- 
tremity, sometimes  the  posterior  extremity  has  been  considered  as  fixed ; 
sometimes  the  mobility  of  both  extremities  was  taken  for  granted 
(Donders),  sometimes  both  were  considered  fixed.  The  oldest  descrip- 
tions seem  to  be  the  best,  especially  that  of  H.  Milller;  most  of  the 
modern  works  seem  influenced  by  the  hypothesis  of  Helmholtz.  Accord- 
ing to  H.  Milller,  we  must  distinguish  between  a  longer  superficial  part 

(fig.  109)  composed  of  longitudinal 
fibres  which  are  inserted  in  front  on 
the  sclera,  near  the  canal  of  Schlemm, 
and  which  are  lost  behind  in  the 
choroid,  and  a  deep  part,  also  com- 
posed in  greater  part  of  longitudinal, 
but  shorter,  fibres,  and  not  going  so 
far  either  in  front  or  behind,  as  the 
superficial  fibres.  These  fibres  are 
not  inserted  in  the  sclera.  The  deep- 
est layer  is  composed  of  oblique  or 
even  circular  fibres.  Milller  thought 
that  they  formed  a  true  sphincter,  but 
the  existence  of  such  a  sphincter  is 
by  no  means  proved;  after  holding 
for  some  time  a  circular  direction, 
these  fibres  seem  to  change  their 
course  and  to  continue  in  the  deep 


Fig.  109.  —  Ciliary  muscle  of  man. 
( After  H.Muller.) 

a,  cornea ;  6,  sclera ;  c,  iris ;  d,  ciliary 
process;  e,  canal  of  Schlemm;  /, 
longitudinal  fibres;  g,  circular 
fibres;  h,  transitional  fibres  of  the 
ciliary  muscle. 


170 


PHYSIOLOGIC  OPTICS 


longitudinal  fibres.  It  seems  that  at  least  a  part  of  the  deep  longitudinal 
fibres  ends  thus ;  others  seem  to  end  free,  without  insertion,  in  the  part 
of  the  muscle  which  goes  towards  the  anterior  chamber. 

By  dividing  a  hardened  eye  into  two  halves  by  a  longitudinal  section, 
we  easily  discover  the  small  white  triangle  of  the  ciliary  muscle.  If  we 
then  exert  a  traction  upon  the  iris  in  order  to  separate  the  ciliary  body 
from  the  sclera,  we  do  not  tear  the  muscle  from  its  insertion  near  the 
canal  of  Schlemm,  but  we  divide  it  into  two  leaflets,  both  of  which  end, 
behind,  in  the  choroid.  In  the  fresh  eye  there  also  always  remains  a  part 
of  the  muscle  adhering  to  the  sclera  as  Mannhardt  had  already  observed. 
When  making  this  experiment  we  produce  an  appearance  which  forcibly 
recalls  the  ciliary  muscle  of  certain  animals  (the  cat,  for  example,  fig. 
no),  in  which  the  muscle  is 
divided  in  front  into  two 
parts  separated  by  a  pro- 
longation backwards  of  the 
space  of  Font  ana. 

Among  the  authors  who 
have  reached  a  result  differ- 
ent from  that  of  Helmholtz, 
I  shall  mention  Mannhardt, 
who,  by  a  study  of  the  com- 
parative anatomy  of  the 
ciliary  muscle,  reached  the 
conclusion  that  it  is  the  pos- 
terior extremity  of  the  mus- 
cle which  should  be  consid- 
ered as  fixed,  and  that  ac- 
commodation must  be  pro- 
duced by  a  traction  exerted 
by  the  ciliary  muscle  on  the 
zonula.  He  was  vigorously 
attacked  by  H.  Mutter,  and 
his  work  scarcely  attracted  attention  because  it  could  not  be  considered 
that  a  traction  on  the  zonula  could  produce  an  increase  of  the 
curvature  of  the  crystalline  surfaces.  We  cite,  moreover,  the  remark- 
able observations  of  Foerster  (1864),  according  to  which  the  tension 
diminishes  in  the  anterior  chamber  during  accommodation.  He  ob- 
served several  patients  in  whom  he  performed  paracentesis  so  that  the 
iris  and  crystalline  lens  were  nearly  in  contact  with  the  cornea.  When 


Fig.  110.  —  Ciliary  part  of  the  eye  of  a  cat. 

a,  Ciliary  muscle  dividing  in  front  into  two 

leaflets ;  b,  canal  of  Fontana  ;  c,  cornea ;  d,  iris. 


ACCOMMODATION  171 

the  patient  made  an  effort  of  accommodation,  the  middle  of  the  cornea 
became  depressed  to  assume  its  old  form  by  the  relaxation  of  the  accom- 
modation. It  must  be  noted,  however,  that  the  phenomenon  persisted 
after  instillation  of  atropine.  In  persons  having  a  corneal  fistula  he 
obtained  an  almost  immediate  effect  from  atropine  by  placing  a  drop 
in  the  conjunctival  sac  and  making  an  effort  of  accommodation,  the 
liquid  being  sucked  into  the  anterior  chamber  by  the  diminution  of 
tension.  These  beautiful  observations,  which  Arlt  declared  equivalent 
to  physiologic  experiments,  are  scarcely  explicable  by  the  theory  of 
Helmholts. 

86.  Personal  Experiments. — Finally  I  come  to  my  own  experiments 
on  accommodation:  the  first  (i°)  are  derived  from  the  statements  of 
Young. 

i°  The  amplitude  of  accommodation  diminishes  tozvards  tJte  periphery  of 
the  pupil. 

a.  ABERROSCOPIC  PHENOMENA.  —  We  have  already  seen  that  with  the 
aberroscope  (see  page  102)  most  persons  see  the  shadows  concave 
towards  the  periphery.  But,  on  making  an  effort  of  accommodation, 
the  form  of  the  shadows  changes:  they  turn  their  concavity  towards 


I  II 

Fig.  111.  —  Change  of  aberroscopic  phenomena  during  accommodation. 
I,  Repose.   II,  Accommodation. 

the  middle,  which  indicates  that  the  refraction  increases  towards  the 
middle  (fig.  in).  After  what  we  have  said  on  page  98  it  follows  that 
the  central  refraction  must  have  increased  more  than  the  peripheral 
refraction. 


172  PHYSIOLOGIC   OPTICS 

Some  people  in  a  state  of  repose  see  shadows  straight  or  slightly  con- 
cave towards  the  middle.  In  such  people  this  deformity  becomes  still 
more  pronounced  during  accommodation. 

b.  CHANGE  OF  THE  CIRCLE  OF  DIFFUSION.  —  If  we  observe  a  distant 
luminous  point,  after  having  made  the  eye  myopic,  it  appears  under  the 
form  of  a  luminous  disc,  the  brightness  of  which  is  generally  uniform  or 
concentrated  at  the  middle.  During  accommodation  we  see  it  change 
its  appearance;  we  see  a  feebly  luminous  disc  surrounded  by  a  bright 
border.  According  to  the  explanation  given  on  page  98,  this  observa- 
tion means,  like  the  preceding  one,  that  the  spherical  aberration  is  over- 
corrected  during  accommodation,  that  is  to  say,  that  the  central  accom- 
modation is  greater  than  the  peripheral  accommodation.  Although 
accommodation  may  increase  the  refraction  of  the  eye  by  many  diop- 
trics, the  circle  of  diffusion  increases  only  slightly,  at  least  when  the 
pupil  is  dilated.  Figure  112  shows  the  appearance  of  the  circle  of  diffu- 
sion of  an  emmetropic  eye ;  rendered  8  D.  myopic  by  a  convex  lens,  this- 


Fig.  112.  —  Appearance  of  the  luminous  point  (right  eye  of  Professor  Koster, 
treated  with  cocaine). 


eye  sees  the  circle  of  diffusion  represented  by  a,  figure  113,  while  b,  same 
figure,  represents  the  form  under  which  it  sees  a  luminous  point  by  mak- 
ing an  effort  of  accommodation  of  8  D.  without  a  lens.  The  pupil  was- 
dilated.  The  explanation  of  the  phenomenon  is  easy :  let  us  imagine  the 
pupil  and  circle  of  diffusion  divided  into  corresponding  zones ;  it  is  clear 
that  if  the  accommodation  is  everywhere  the  same,  all  the  zones  of  the 


ACCOMMODATION  173 

diffusion  circle  ought  to  increase,  while,  if  the  accommodation  dimin- 
ishes towards  the  periphery,  the  outside  zones  increase  little  or  nothing 
and  the  central  zones,  on  increasing,  come  to  partly  cover  the  peripheral 
zones.  This  is  the  reason  why  the  circle  of  diffusion  is  surrounded  dur- 


Fig.  113.  —  The  same  eye  as  in  figure  112. 

a,  Appearance  of  the  luminous  point,  the  eye  being  rendered  myopic  8  D.  with  a  convex 
lens  (Repose).  6,  Appearance  of  the  luminous  point,  without  lens,  the  eye  accommo- 
dating 8  D. 

Measured  with  the  optometer  of  Young,  the  central  accommodation  was  8  D. ;  the  pe- 
ripheral accommodation  (at  2.5mm  from  the  axis)  was  3.3  D. 

ing  accommodation  with  a  bright  border,  without  increasing  much  in 
diameter. 

c.  MEASUREMENT  WITH  THE  OPTOMETER  OF  YOUNG.  —  The  opto- 
meter of  Young  enables  us  to  measure  directly  the  difference  between 
the  central  accommodation  and  peripheral  accommodation. 

We  measure  the  central  accommodation  with  the  two  nearest  slits 
(see  page  102),  which  we  place  as  nearly  as  possible  at  the  middle  of  the 
pupil,  and  the  peripheral  accommodation  with  the  triangular  plate  which 
we  lower  just  enough  to  be  able  to  still  see  the  two  lines.  In  this  way 
we  prove  that  at  the  border  of  the  pupil  (supposed  to  be  five  millimeters) 
the  amplitude  of  the  accommodation  is  only  half  the  central  accommodation 
or  still  less.  If,  after  having  dilated  my  pupil  to  the  utmost  (with  a  mixture 
of  cocaine  and  homatropine),  I  use  an  interval  of  7  millimeters,  my  ac- 


174  PHYSIOLOGIC  OPTICS 

commodation  which,  at  the  middle  of  the  pupil,  is  2.5  D.  to  3  D.,  dimin- 
ishes nearly  to  zero  (0.2  D.)  on  the  borders.  Here  are  some  measure- 
ments: 


Central  amplitude 
(interval  0.75  mm.). 
9.8  D. 

Peripheral  amplitude 
(interralSmm.). 

4.2    D. 

8     D. 

3.3    D. 

7.5  D, 

3.7    D. 

6     D.  (1) 

3       D. 

4     D  (1) 

2       D. 

Mme  T  

6.7  D. 

3.8    D. 

Tschernine  .  . 

3     D. 

1.25  D. 

We  find  still  more  considerable  differences  between  the  central  and 
peripheral  accommodation,  by  placing  the  two  slits  sometimes  at  the 
middle  of  the  pupil,  sometimes  near  the  borders: 


AMPLITUDE  OF   ACCOMMODATION 


Temporal  border.  Center.  Nasal  border. 

Demicheri  (Homatropine) 6     D.  2  D. 

0  4     D.  (1)         ID. 

MmeT 5       D.  6.7  D.  5  D. 

Tscherning  (Homatropine) 0. 25  D.  3     D.  0 

d.  SKIASCOPIC  EXAMINATION.  —  Observations  a  and  b  are  easy  to 
make,  but  they  require  that  the  observer  be  young,  that  his  pupil  be 
well  dilated  and  that  he  be  master  of  his  accommodation ;  observations 
with  the  optometer  of  Young,  as  well  as  those  with  the  ophthalmometer, 
which  I  shall  describe  forthwith,  are  quite  delicate  and  require  special 
instruments.  But  we  possess  in  skiascopy  with  a  luminous  point  a  very 
convenient  means  of  studying  the  nature  of  accommodation.  To  make 
the  observation  we  select  a  child  or  a  young  person  whose  pupil  is  well 
dilated  with  cocaine.  It  is  better  to  select  a  person  whose  pupil  is  well 
dilated,  who  is  almost  emmetropic,  and  who  has  not  too  much  aberra- 
tion in  a  state  of  repose.  We  place  the  lamp,  surrounded  with  its  perfo- 
rated screen,  at  one  side  of  and  a  little  behind  the  observed  person  and 
we  project  light  on  his  eye  by  means  of  a  concave  mirror,  which  forms 
the  image  of  the  opening  at  15  to  20  cm.  from  the  observed  eye,  in  which 
position  we  place  a  mark  of  fixation.  As  long  as  the  observed  person 
does  not  accommodate,  the  condition  of  Jackson  is  not  fulfilled,  and  we 
see  the  pupil  entirely  illuminated,  but  at  the  moment  when  the  observed 
person  fixes  the  fixation  mark  the  ring  of  over-corrected  aberration 
appears  with  all  desirable  distinctness.  The  phenomenon  is  espe- 

(1)  The  accommodation  was  weakened  by  the  influen     of  homatropine. 


ACCOMMODATION  175 

cially  striking  if  we  compare  the  appearance  of  the  accommodated  eye 
with  that  of  the  non-accommodated  eye,  made  myopic  with  a  convex 
glass  (fig.  1130).  We  have  observed  (page  99)  that  we  see  luminous, 
under  these  circumstances,  the  parts  of  the  observed  pupil  which  send 


Fig.  113a.  —  Skiascopic  examination  of  accommodation,  a,  Appearance  of  the  emmetropic  eye 
made  myopic  with  a  lens  of  -{-  5  D.  6,  Appearance  of  the  same  eye,  accommodating 
5  D.  without  lens. 

light  into  the  observing  eye.  Placed  at  50  cm.  the  existence  of  the  ring 
indicates,  therefore,  that  there  are,  towards  the  borders  of  the  pupil, 
parts,  the  myopia  of  which  does  not  exceed  2  D.,  for  otherwise  the  rays 
proceeding  from  these  parts  would  have  already  crossed  the  axis,  and 
would  not  enter  into  the  observing  eye.  To  determine  the  degree  of 
aberration  produced  by  accommodation,  we  approach  nearer  and  nearer 
the  point  of  fixation ;  the  ring  becomes  thinner  and  thinner,  but  it  is  rare 
that  it  disappears  completely  before  the  accommodation  attains  a  very 
high  degree.  I  have  thus  shown  that  a  central  accommodation  of  8  D. 
accompanied  a  peripheral  accommodation  of  2  D.  in  a  case  in  which  the 
pupil  was  very  large.  The  condition  was,  therefore,  still  more  pro- 
nounced than  in  the  cases  which  I  examined  writh  the  optometer.  The 
phenomena  may  present  themselves  a  little  differently  if  the  positive 
aberration  is  very  pronounced  in  a  state  of  repose,  but  on  making  the 
calculations  we  obtain  the  same  result. 

2°  During  accommodation  the  anterior  surface  of  the  crystalline  lens  in- 
creases in  curvature  at  the  middle,  while  it  is  flattened  towards  the  periphery. 

I  place  the  arc  of  the  ophthalmophakometer  horizontally,  and  attach 
three  incandescent  lamps  to  it,  so  that  they  are  on  the  same  horizontal 
line  and  just  far  enough  apart  for  all  three  images  formed  by  the  anterior 
surface  of  the  crystalline  lens  to  be  visible  in  the  pupil.  I  direct  the  look 
of  the  observed  person  so  that  the  three  images  are  situated  near  the 


176 


PHYSIOLOGIC   OPTICS 


upper  border.  In  a  state  of  repose  they  are  arranged  in  a  straight  line 
(fig.  1 14  a)  or  following  a  curve  slightly  concave  towards  the  center  (fig. 
115  A);  during  accommodation,  they  form  a  curve  convex  towards  the 


a  bl  62  b3 

Fig.  114.  —  Reflection  images,  on  the  anterior  surface  of  the  crystalline  of  my  right  eye, 
of  three  lamps  placed  on  a  horizontal  line,  a,  in  a  state  of  repose;  bl  b2  63,  in  different 
stages  of  accommodation.  Highest  accommodation  3  D.  with  cocaine. 

middle  (fig.  114  blt  b2,  63,  115  B),  and  the  curvature  of  which  is  more 
pronounced  in  proportion  as  the  accommodation  is  greater. 

It  is  easy  to  see  that  this  phenomenon  indicates  a  greater  curvature 
at  the  middle  than  towards  the  periphery :  indeed,  let  us  suppose  for  an 
instant  that  we  have  added  three  other  lamps,  which  would  form  their 
images  near  the  lower  border  of  the  pupil,  and  let  us  consider  as  objects 


Fig.  115.  —  Reflection  images  of  the  right  eye  of  Mme  T.  —  A,  in  a  state  of  repose ;  B, 
during  accommodation  (after  a  drawing  of  Professor  Hosier}.  —  a,  corneal  images;  b, 
images  of  anterior  surface  of  the  crystalline  lens.  Accommodation  of  6  D. 

the  distances  between  the  two  lamps  situated  on  the  same  vertical  line. 
We  would  thus  have  three  equal  objects,  the  images  of  which  would 
be  of  the  same  size  in  a  state  of  repose  (aa,  fig.  116),  which  indicates  that 
the  curvature  is  the  same  everywhere ;  but,  during  accommodation,  the 
image  (b,  fig.  116)  of  the  middle  is  considerably  smaller  than  the  other 
two,  b±  bit  which  indicates  that  the  curvature  is  greater  at  this  place. 

We  observe  an  analogous  phenomenon  on  the  cornea,  in  cases  of 
keratoconus.  The  keratoscope  of  De  Wecker  and  Masselon  is  formed  by 
a  white  square  on  a  black  ground.  On  examining  a  case  of  keratoconus 
with  this  instrument,  and  causing  the  look  to  be  so  directed  that  the 


ACCOMMODATION 


177 


apex  of  the  keratoconus  coincides  with  the  axis  of  the  instrument,  we 
see  the  sides  of  the  image  of  the  square  assume  the  form  of  curves 
turning  their  convexity  towards  the  middle  (fig.  117). 


Repose 


Accommodation 


Fig.  116. 


We  might  think,  from  these  phenomena,  that  the  curvature  of  the 
peripheral  parts  increases  during  accommodation,  but  less  than  that  of 


Fig.  117.  —  Deformity  of  the  corneal  image  of  a  white  square  in  a  case  of  keratoconus. 

(After  Masselon.) 

the  central  part.  Nothing  of  the  kind:  the  peripheral  parts  undergo  a 
real  flattening  which  causes,  however,  an  increase  of  refraction.  To 
understand  this  fact,  which  might  appear  paradoxical,  we  must  recall 
what  I  have  said  on  page  13  on  refraction  by  surfaces  of  the  second 
degree.  Outside  of  the  axis,  it  is  the  normal  and  not  the  radius  of 
curvature  which,  for  refraction  (and  also  for  reflection),  plays  the  part 
of  the  radius  of  the  sphere,  supposing  that  the  luminous  point  (or,  in 
the  case  of  reflection,  the  observing  eye)  is  on  the  axis. 

In  figure  118,  BDE  represents  a  curve  of  the  second  degree,  AF  its 
axis,  BH  the  radius  of  curvature  at  the  point  B,  BG  the  normal  at  this 


178 


PHYSIOLOGIC   OPTICS 


point  and  the  dotted  curve  a  circle  drawn  with  BG  as  radius.  The 
luminous  ray  AB  is  refracted  in  the  direction  BF,  exactly  as  if  the  sur- 
face were  replaced  by  the  circle  BE. 

The  measurements  which  we  have  made  with  the  optometer  of  Young 
enable  us  to  calculate  approximately  the  form  of  the  surface,  and  the 
calculation  will  explain  at  the  same  time  what  I  have  just  said.  Let  us 
suppose  that  all  the  accommodation  is  effected  by  the  anterior  surface, 
and  let  us  take  the  experiment  of  Demicheri  as  an  example.  He  had,  at 
the  middle,  an  accommodation  of  7.5  D.,  at  2.5  mm.  from  the  axis  an 
accommodation  of  3.7  D.  Let  us  suppose  10  millimeters  for  the  radius 


Fig.  118.  —  Refraction  by  a  parabolic  surface. 

of  the  anterior  surface  in  a  state  of  repose  and  1.06  for  the  index  of  the 
crystalline  lens  in  relation  to  the  aqueous  humor.  We  express  the  refrac- 
tion of  the  surface  by  the  inverse  of  the  anterior  focal  distance  -~  =  —-- 
—  oToicrs  =  6  D.  During  accommodation  the  central  refraction  increased 
7.5  D. ;  the  refraction  of  the  surface  would  be,  therefore,  at  this 
place  13.5  D.  Whence  we  obtain  the  radius  pQ  by  the  formula  n"~J=M6 

Po  Po 

=  13.5  D.,  which  gives  p0  =  4.44.  At  2.5  mm.  from  the  axis  the 
accommodation  was  3.7  D.,  the  refraction  of  the  surface  in  a  state  of 
accommodation  6  D.  -f  3.7  D.  =  9.7  D.,  and  the  normal  N,  at  this  place, 
would  be  found  by  the  formula  ~  =  9.7  =  -~  ,  which  gives  N  =  6.1  mm. 
We  can  then  find  the  radius  of  curvature  p ,  at  this  place,  by  the  formula 

1C  3 

P  s=s  ^i »  wm'cn  holds  good  for  all  surfaces  of  the  second  degree.  It  gives 
P  =  12  millimeters.  We  see  that  the  surface  is  already  flattened  at  this 
place  during  accommodation,  and  it  is  manifestly  flattened  still  more 
farther  towards  the  periphery.  If  a  small  part  of  the  accommodation  is 
effected  by  the  posterior  surface,  as  is  probable,  the  flattening  of  the 
anterior  surface  towards  the  periphery  must  be  still  greater,  for  it  is 


ACCOMMODATION 


179 


probable  that  the  part  of  the  accommodation  which  is  due  to  the  pos- 
terior surface  diminishes  relatively  much  less  quickly  towards  the  pe- 
riphery. Supposing  that  the  portion  of  the  accommodation  due  to  the 
posterior  surface  be  i  D.,  as  well  at  the  center  as  near  the  border  of  the 
pupil,  we  would  have  for  the  anterior  surface  /><>  =  4.8  mm.,  p  =  14.2  mm. 

The  surface  would  have  the  form  of  a  quite 
flattened  hyperboloid  (fig.  119),  the  apex  of 
which  would  correspond  very  nearly  with 
the  optic  axis  of  the  eye,  and  would  be 
found  a  little  outside  the  visual  line.  It  is 
interesting  to  observe  that  among  all  the 
surfaces  of  the  second  degree  having  p0  = 
4.8  mm.,  it  is  this  hyperboloid  which  most 
nearly  approaches  the  form  of  the  surface 
in  a  state  of  repose.  Accommodation  is 
effected,  therefore,  by  a  minimum  de- 
formity. 

3°  By  placing  the  cursor  A  of  the  oph- 
thalmophakometer  above  the  telescope, 
and  requesting  the  observed  person  to  look 
towards  the  latter,  we  observe,  when  he 
makes  an  effort  of  accommodation,  the  fol- 
lowing phenomena  (fig.  120) : 

I.  The  image  of  the  anterior  surface  of 
the  crystalline  descends  quickly  towards 
the  corneal  image,  and  is  finally  hidden  be- 
hind the  latter.     It  is  this  displacement 
which    has    been    described    by    Cramer. 
Towards  the  end  of  this  phase  the  pupil- 
lary contraction  begins. 

II.  This  movement    ended,    the    small 
image  of  the  posterior  surface  of  the  crys- 
talline descends  in  its  turn  by  a  slow  and  abrupt  movement.     Its  dis- 
placement is  much  less  than  that  of  the  large  image ;  and,  while  the  latter 
moves  in  a  straight  line,  the  small  image  is  displaced  in  a  curve  with  its 
concavity  turned  towards  the   middle.     The  pupillary  contraction  is 
greatest  during  this  phase. 

III.  When  the  observed  person  relaxes  his  accommodation,  the  small 
image  again  ascends  to  resume  its  old  place  with  a  quick  movement,  as 
if  moved  by  a  spring. 


Fig.  119. — Deformity  of  the  crys- 
talliue  surfaces  during  accomo- 
dation.  The  full  curves  indi- 
cate the  shape  in  a  state  of  repose, 
the  dotted  curves  the  accommo- 
dative shape.  (Accommodation 
7D.) 


180 


PHYSIOLOGIC  OPTICS 


IV.  This  movement  ended,  the  large  image  re-ascends  in  its  turn ;  its 
movement  is  rather  slow,  and  as  if  hesitating. 

The  accommodative  phenomena  seem,  therefore,  to  take  place  in  two 
steps.  i  "  in  tv 


Fig.  120.  —  The  four  apparent  phases  of  accommodation.  •  Corneal  image.  —  O  Image  of 
the  anterior  surface  of  the  crystalline.  —  •  Image  of  the  posterior  surface  of  the  crys- 
talline. A,  accommodation  ;  B,  relaxation. 


Fig.  121.  —  Eight  eye  of  Mme  T.  —  Displacements  of  the  image  of  the  posterior  surface 
during  accommodation,  observed  with  the  ophthalmophakometer.  C,  by  fixing  the 
telescope;  D,  by  looking  to  the  right;  G,  by  looking  to  the  left;  H,  by  looking  up- 
wards ;  B,  by  looking  downwards.  —  The  large  white  spot  is  the  corneal  image,  the 
two  small  white  spots  indicate  the  position  of  the  image  of  the  posterior  surface  of  the 
crystalline  in  a  state  of  repose  and  during  accommodation.  The  arrows  indicate  the 
direction  of  the  displacement  which  takes  place  when  an  effort  of  accommodation  is 
made. 


ACCOMMODATION  181 

During  the  displacement  of  the  small  image,  the  large  one  is  con- 
cealed behind  the  corneal  image,  so  that  we  cannot  see  whether  it  is 
displaced  or  not;  it  is  not  easy  to  find  a  direction  of  the  look  such  that 
we  can  follow  the  two  crystalline  images  during  the  entire  accommoda- 
tive displacement.  Sometimes  they  are  concealed  behind  the  corneal 
image,  sometimes  behind  the  iris.  I  have,  however,  succeeded  in  doing 
so  by  using  two  lamps,  one  for  each  image ;  in  this  way,  we  can  satisfy 
ourselves  that  the  large  image  undergoes  a  slight  displacement  down- 
wards at  the  same  time  as  the  small  one,  but  this  displacement  of  the 
large  image  is  concealed  by  the  corneal  image  when  we  perform  the 
experiment  as  I  have  just  described.  It  is  especially  easy  to  observe  the 
displacement  downwards  of  the  large  image,  if  the  direction  of  the  look 
of  the  observed  person  is  such  that  the  image  in  repose  is  placed  near 
the  internal  or  external  border  of  the  pupil.  The  movement  of  Cramer 
then  takes  place  in  a  horizontal  direction.  Having  reached  the  end,  the 
image  makes  a  bend,  becoming  displaced  a  little  downwards,  but  this 
latter  displacement  is  much  less  than  that  of  the  small  image.  I  may  add 
that  the  small  image  is  displaced  downwards,  whatever  may  be  its  posi- 
tion in  the  pupil  (fig.  121),  which  indicates  that  the  cause  can  be  sought 
neither  in  the  increase  of  curvature  of  the  surface,  nor  in  a  displacement 
forwards  or  backwards  of  the  crystalline  lens.  But  this  displacement 
downwards  of  the  image  is  combined  with  a  quite  small  centripetal  dis- 
placement, which  also  takes  place  whatever  may  be  the  position  of  the 
image  in  the  pupil,  and  which  is  probably  due  to  a  slight  recession  of  the 
posterior  surface. 

The  observation  has  again  been  made  by  Hess  and  Heine.  They  have 
found  that  the  displacement  of  the  small  image  takes  place  downwards, 
whatever  may  be  the  position  of  the  head ;  if  we  lean  the  head  on  the 
right  shoulder,  the  displacement  of  the  small  image  takes  place  towards 
the  side  which  is  downwards,  that  is  to  say,  for  the  right  eye  towards 
the  temporal  border  of  the  pupil,  for  the  left  eye  towards  the  nasal 
border.  I  was  able  to  verify  this  observation,  which  seems  to  indicate 
that  the  change  takes  place  under  the  influence  of  the  weight.  Hess  also 
observed  that  an  entoptic  figure,  situated  on  the  posterior  surface  of  the 
crystalline  lens,  is  displaced  downwards  by  a  maximum  accommodation, 
whatever  may  be  the  position  of  the  head. 

4°  Other  Phenomena  Accompanying  Accommodation.  —  We  have  seen 
that  Hueck  discovered  a  slight  advancement  of  the  anterior  surface; 
Helmholtz  confirmed  this  observation.  It  is  possible  that  we  may  some- 
times meet  such  a  displacement,  although  the  experiment  of  Helmholtz 


182  PHYSIOLOGIC  OPTICS 

did  not  succeed  very  well  with  me.  and  although  I  am  not  sure  that  his 
observations  do  not  admit  of  another  explanation.  In  the  eye  with 
which  I  have  made  my  experiments,  the  anterior  surface  did  not  ad- 
vance ;  the  part  corresponding-  to  the  pupil  did  not  change  its  place,  but 
the  part  covered  by  the  iris  receded  with  this  membrane.  There  is 
formed  during  accommodation,  at  the  anterior  surface  of  the  iris,  a 
circular  depression  (fig.  122),  the  peripheral  border  of  which,  corre- 
sponding to  the  ciliary  body,  rises  in  a  peak,  while  the  central  border  pre- 
sents a  very  gentle  slope,  corresponding  to  the  anterior  surface  of  the 
crystalline  lens.  I  commend  this  observation,  which  was  already  made 
by  Cramer,  but  which  has  often  been  regarded  as  proving  an  enlarge- 
ment of  the  anterior  chamber  in  the  angle  of  the  iris ;  it  is  easy  to  see 
that  the  most  peripheral  parts  of  the  posterior  partition  of  the  anterior 
chamber  do  not  recede.  The  phenomena  are  not  always  equally  pro- 
nounced, but  we  can  nearly  always  find  at  least  a  trace  of  them  in  young 
subjects.  We  can  make  the  observation  by  oblique  illumination,  but  the 
use  of  the  magnifying  glass  (monocular)  is  not  to  be  recommended; 
binocular  vision  is  necessary  in  order  to  properly  account  for  the  change 
in  the  level  of  the  iris.  When  the  phenomenon  is  quite  pronounced,  we 
thus  obtain  a  quite  distinct  idea  of  the  conical  form  which  the  anterior 
crystalline  assumes  during  accommodation. 

As  to  the  posterior  surface  of  the  crystalline  lens,  its  changes  are  less 
manifest.  We  have  seen  that  the  catoptric  phenomena  seem  to  indicate 
a  slight  increase  of  curvature.  The  posterior  surface  remains  very 
nearly  in  its  place  during  accommodation ;  sometimes,  however,  we  ob- 
serve phenomena  which  seem  to  indicate  that  it  recedes  a  little. 


Fig.  122.  —  Change  of  the  anterior  chamber  during  accommodation ;  a,  repose  ; 

b,  accommodation. 

The  much-discussed  question  of  knowing  whether  the  thickness  of  the 
crystalline  lens  changes  during  accommodation  is  very  difficult  to  decide, 
because  the  change,  if  it  exists,  does  not  exceed  the  limit  of  an  error  of 
observation.  Influenced,  perhaps,  by  the  observation  of  Helmholts,  I 
had  thought  an  increase  of  thickness  established.  Recently  I  took  up 
the  subject  anew  in  collaboration  with  Professor  Koster;  we  went  to 
much  trouble  without  being  able  to  reach  a  definite  result. 


ACCOMMODATION  183 

87.  The  Author's  Theory  of  Accommodation.  —  After  the  observations 
which  I  have  just  described  in  the  preceding  paragraph,  and  which  can 
be  briefly  expressed  by  saying  that  accommodation  is  effected  by  the  tempo- 
rary formation  of  an  anterior  le-nticonus,  the  hypothesis  of  Helmholts  does 
not  seem  tenable ;  for  it  is  not  easy  to  conceive  how  such  a  mechanism 
could  produce  a  flattening  of  certain  parts  of  the  crystalline  lens  and  at 
the  same  time  an  increase  of  curvature  of  the  other  parts. 

I  have  already  observed  that  the  curvature  of  the  anterior  surface  of 
the  crystalline  lens  of  the  dead  eye  corresponds  with  that  of  the  living 
crystalline  lens  in  a  state  of  repose,  and  not  at  all  with  the  accommodated 
crystalline  lens.  But  the  difference  between  the  dead  crystalline  lens  and 
the  accommodated  crystalline  lens  is  still  more  striking,  if  we  consider 
not  only  the  curvature  at  the  middle,  but  the  form  of  the  entire  surface, 
because  the  anterior  surface  of  the  accommodated  crystalline  lens  is 
flattened  towards  the  borders,  as  I  have  just  explained;  in  the  dead  eye 
the  curvature,  on  the  contrary,  increases  considerably  towards  the 
borders,  the  surface  having  the  form  of  an  ellipsoid  of  revolution  around 
the  short  axis.  This  fact,  which  was  already  established  by  Krause,  (i) 
is  especially  very  striking  if  we  examine  the  eye  with  the  ophthalmo- 
meter,  as  I  explained  on  page  61.  The  most  usual  way  is  to  remove 
the  prism,  and  observe  the  image  of  the  keratoscopic  disc.  As  long  as 


CAB 

Fig.  122a.  —  Reflection  images  on  the  anterior  surface  of  the  dead  crystalline  len*.  A,  at  the  center ; 

B  and  C,  towards  the  borders. 

the  ophthalmometer  is  placed  in  the  direction  of  the  axis  of  the  crystal- 
line lens,  the  images  of  the  circle  are  round,  but,  if  we  displace  the  in- 
strument so  as  to  form  the  image  near  the  border,  it  changes  into  an 

(1 )  Hclmholtz  seems  to  have  been  lecl  into  error  by  the  celebrated  measurements  which  Jean  Louis  Petit 
had  made  at  the  commencement  of  the  eighteenth  century.  Most  of  the  measurements  of  Petit  are  very 
exact,  but  those  of  the  curvatures  of  the  surfaces  are  without  any  value.  He  had  a  series  of  copper 
plates  cut  in  the  form  of  arcs  of  circles  of  different  radii.  His  only  means  of  determining  the  curvature 
of  the  surfaces  of  the  eye  consisted  in  finding  the  arc  of  the  circle  which  seemed  to  him  to  conform  to 
the  surface.  The  measurements  of  Krause  are  astonishingly  good  if  we  consider  the  manner  in  which 
he  made  them.  He  cut  a  fresh  eye  in  two,  along  the  axis,  placed  one-half  of  it  in  water  under  a  micro- 
meter and  examined  with  a  microscope  of  little  magnifying  power. 


184  PHYSIOLOGIC  OPTICS 

ellipse  with  the  long  axis  vertical.  Comparing  figure  1220,  with  those  on 
page  62,  we  see  that  the  deformity  of  the  surface  is  quite  the  contrary 
of  the  conical  form.  —  Following  are  the  radii  of  curvature  from  5°  to  5° 
of  an  eye  measured  by  Holth,  compared  with  those  which  I  have  cal- 
culated for  the  eye  of  Demicheri  in  maximum  accommodation: 

Age          o°  5°  10°          15°          20° 

Dead  eye 28        12,4mm        12mm        llmm          9mm          7mm 

Accommodated  eye.. ..         25          5.6mm          5.9mm       7.0mm     18.0mm     79.2mm 

We  see  that  we  can  scarcely  suppose  a  more  pronounced  difference 
(fig.  I22b).     I,  therefore,  set  myself  to  study  the  physical  qualities  of  the 


Fig.  1226.  —  A,  the  dead  crystalline  lens ;  B,  the  accommodated  crystalline  lens.  The  dotted 
lines  indicate  the  form  of  the  surfaces  of  the  second  degree,  to  which  the  majority  of 
crystalline  surfaces  most  nearly  approach. 

crystalline  lens,  by  using  especially  the  lenses  of  horses,  which  are  very 
large  and  consequently  easily  handled,  and  I  have  found  that  we  cannot 
consider  the  crystalline  lens  as  a  simple  elastic  body  in  the  sense  of 
Helmholtz.  The  contents  of  the  crystalline  lens  are  composed,  in  the 
adult,  of  two  parts,  the  nucleus,  which  cannot  change  its  form,  and  the 
superficial  layer  which,  on  the  contrary,  possesses  this  faculty  to  a 
very  high  degree;  its  consistence  is  very  nearly  that  of  a  solution  of 
very  thick  gum.  I  call  this  layer  the  accommodative  layer  in  order  to  show 
that  it  is  due  to  it  that  the  eye  can  accommodate  itself.  According  a% 
age  advances,  the  nucleus  increases  while  the  accommodative  layer 


ACCOMMODATION 


185 


diminishes  and  with  it  the  amplitude  of  accommodation.  The  whole  is 
surrounded  by  a  capsule  which  is  inextensible  or  very  nearly  so  (Hoc- 
guard). 

It  has  always  been  supposed  that  a  traction  exerted  on  the  zonula 
must  flatten  the  crystalline  surfaces,  while  a  pressure  exerted  on  the 
borders  would  have,  on  the  contrary,  the  effect  of  increasing  their  curva- 
ture. Nothing  of  the  kind :  a  pressure  exerted  on  the  borders  has,  on 
the  contrary,  the  effect  of  flattening  the  surfaces,  while  a  traction 
exerted  on  the  zonula  increases  the  curvature  of  the  surfaces  at  the 
middle,  while  flattening  them  towards  the  periphery. 

To  verify  this  fact  we  take  the  crystalline  lens  from  the  eye  of  an  ox 
or  a  horse,  which  must  not  be  too  old,  with  the  capsule  and  zonula  of 
Zinn.  It  is  easy  to  see  that  by  compressing  the  borders  the  surfaces 
are  flattened;  to>  observe  the  effect  of  traction  we  take  hold  of  the 
zonula  on  both  sides,  very  near  the  crystalline  lens,  and,  by  pulling,  we 
can,  on  looking  at  the  crystalline  lens  sideways,  see  that  the  anterior 
surface,  assumes  a  hyperbolic  form  (fig.  123).  But  we  obtain  a  better 
idea  of  the  deformity  by  studying  the  catoptric  images.  We  place  the 
crystalline  lens  with  the  anterior  surface  uppermost  on  a  table  and  fix 
above  it,  at  some  distance,  an  opaque  ring  on  which  we  have  stretched 
a  sheet  of  transparent  paper;  by  illuminating  this  sheet  of  paper  we  see 

the  catoptric  image  of  the  ring 
formed  on  the  anterior  surface  of 
the  crystalline  lens  as  a  black  circle. 
We  can  also  replace  the  ring  by  a 
big  lens.  The  size  and  distance  of 
the  ring  must  be  chosen  so  that 
the  image  may  be  sufficiently  large, 
and  placed  so  that  the  image  may 
be  centered  with  the  crystalline 
lens.  Then,  by  exerting  a  traction 
we  see  the  circle  change  into  an 
oval,  the  short  axis  of  which  cor- 
responds with  the  direction  of  the 
traction,  which  proves  that  the 
curvature  increases  in  that  direc- 
tion. The  experiment  succeeds  the 
more  easily  the  larger  the  ring. 
If  we  place  the  ring  so  that  its  image  is  near  the  border  of  the  crystal- 
line lens,  we  see  it  lengthen  in  the  direction  of  the  traction,  which  indi- 


Fig.  123.  —  Crystalline  lens  of  the  ox  twice 
enlarged:  The  dotted  line  indicates  the 
form  which  the  crystalline  lens  assumes: 
A,  by  a  lateral  pressure ;  B,  by  a  traction 
exerted  on  the  zonula.  The  arrows  indi- 
cate the  direction  of  the  forces. 


186 


PHYSIOLOGIC  OPTICS 


cates  a  flattening  in  this  direction.  Dr.  Crzcllitzer  has  recently  con- 
structed an  instrument  by  means  of  which  we  can  exert  a  traction  on 
the  zonula  in  all  directions  at  once,  and  with  which  we  can  still  better 
imitate  accommodation.  Instead  of  the  ring  we  may  use  two  candles 
placed  so  that  their  images  are  in  the  direction  of  the  traction;  on 
stretching  we  see  them  make  a  centripetal  movement  analogous  to  the 
movement  discovered  by  Cramer,  but  much  less  extended.  Indeed,  on 
the  one  hand,  it  is  probable  that  these  animals  (i)  have  not  a  very  well 
developed  accommodation,  and  on  the  other  hand,  it  must  not  be  for- 
gotten that  in  the  eye  the  displacement  appears  nearly  doubled  by  the 
magnifying  action  of  the  cornea.  The  experiment  can  be  considered 
only  as  an  imitation  of  accommodation  on  a  large  scale ;  but  the  fact  that 
we  can  obtain  an  increase  of  curvature  by  a  traction  exerted  on  the 
zonula  is  beyond  doubt. 

Furthermore,  we  should  scarcely  expect  any  other  result.  I  have 
several  times  emphasized  the  fact  that  the  nucleus  has  a  much  more 
pronounced  curvature  than  the  surfaces  of  the  crystalline  lens,  and  more- 
over, that  it  cannot  change  its  form  unless  we 
crush  it.  Glancing  at  figure  124,  we  readily 
understand  that  by  exerting  a  traction  on  the 
zonula  the  peripheral  parts  must  flatten,  while 
at  the  middle  the  curvature  increases  on  ac- 
count of  the  greater  resistance  and  curvature 
of  the  nucleus.  And  the  result  will  be  the  same 
if  there  is  no  nucleus,  as  is  the  case  in  young 
people,  only  if  the  curvature  and  resistance  in- 
crease towards  the  center.  The  increase  of 
curvature  of  the  central  layers  is  visible  on 
any  preparation  of  the  crystalline  lens.  The 
increase  of  resistance  finds  its  optic  expression  in  the  increase  of  index 
towards  the  center. 

By  traction  on  the  zonula  we  have  obtained  changes  analogous  to 
those  which  we  observe  during  accommodation,  and  it  seems  to  me  that 
the  structure  of  the  ciliary  muscle  lends  itself  very  well  to  the  produc- 
tion of  such  traction.  We  have  seen  that  it  is  composed,  for  the  most 

(1)  Dr.  Stadfddt  later  verified  the  results  with  human  crystalline  lenses,  which  he  placed  in  a  cork 
ring,  fixing  two  opposite  parts  of  the  zonula  with  very  fine  needles.  He  measured  the  curvature  of  the 
surfaces  with  the  ophthalrnometer  ofJaval  and  Schioetz,  and  then  determined  the  position  of  the  focus, 
or  rather  that  of  the  focal  lines,  with  a  microscope.  In  consequence  of  the  traction,  he  always  caused 
astigmatism,  the  maximum  of  curvature  corresponding  to  the  direction  of  the  traction.  On  a  crystal- 
line lens  belonging  to  a  person  aged  38  years,  he  thus  produced  an  astigmatism  of  the  anterior  surface 
of  4  D.  The  posterior  surface  was  only  very  slightly  influenced.  —  The  astigmatism  disappeared  with 
the  traction. 


Fig  I'j4.  —  Optic  system  of 
the  eye  of  the  ox  (magnified 
twice). 


ACCOMMODATION  187 

part,  of  longitudinal  fibres,  that  the  most  superficial  fibres  are  inserted 
in  front  on  the  sclera,  near  the  canal  of  Schlemm,  while  the  middle  fibres 
end  free  near  the  surface  which  lies  towards  the  anterior  chamber,  and 
that  the  deepest  fibres  are  combined  with  the  oblique  and  circular  fibres 
which,  perhaps,  form  their  terminations.  The  muscle  has  the  form  of 
a  little  triangle,  the  external  surface  of  which  rests  on  the  sclera,  while 
the  internal  surface  is  turned  towards  the  vitreous  body  and  the  anterior 
surface  towards  the  anterior  chamber.  During  contraction  the  antero- 
external  angle  remains  fixed,  the  antero-internal  angle  recedes,  as  we 
can  see  directly  in  the  anterior  chamber,  and  the  posterior  extremity 
advances  as  the  experiments  of  Hensen  and  Voclkers  prove.  The  reces- 
sion of  the  anterior  part  exerts  on  the  zonula  the  traction  which  pro- 
duces the  deformity  of  the  anterior  surface;  the  advancement  of  the 
posterior  extremity  exerts  on  the  choroid  a  traction  which  has  the  effect 
of  sustaining  the  vitreous  body  and  indirectly  the  crystalline  lens,  so 
that  the  latter  does  not  recede  under  the  influence  of  the  traction.  As 
far  as  the  actual  result  is  concerned,  it  matters  little  to  which  of  the  two 
actions  we  attach  the  greater  weight.  Let  us  conceive,  for  example, 
a  moment  when  the  anterior  extremity  may  be  fixed :  the  result  of  the 
contraction  of  the  muscle  would  be  that  the  crystalline  lens,  on  account 
of  the  traction  exerted  on  the  choroid,  would  be  pushed  a  little  forward, 
which  would  produce  also  a  traction  on  the  zonula,  which  would  suffice 
for  the  deformity  of  the  crystalline  surface.  It  may  be  that  there  exist, 
in  this  relation,  individual  differences  as  the  disagreement  between  the 
observations  of  Helmholtz  and  my  observations  seems  to  indicate,  (i) 

I  think  that  this  theory  explains  quite  satisfactorily  the  greater  part 
of  the  phenomena  which  accompany  accommodation.  It  explains,  in 
the  first  place,  the  deformity  of  the  anterior  surface;  the  direction  of 
the  zonula  in  the  living  eye  is  such  that  the  effect  of  the  traction  must 
act  almost  exclusively  on  the  anterior  surface.  It  explains  also  the 
change  of  level  of  the  iris  and  the  diminution  of  tension  of  the  anterior 
chamber  (by  the  recession  of  the  peripheral  parts  of  the  crystalline  lens 
and  iris). 

The  phenomena  observed  by  Coccius  are  probably  due  to  an  optic 


(1)  According  to  certain  authors  (Arlt,  Iwanoff),  the  ciliary  muscle  differs  in  myopes  and  hyperme- 
tropes.  If  this  is  so,  we  might,  perhaps,  find  the  predisposition  to  myopia  in  a  special  structure  of  the 
ciliary  muscle.  It  is,  indeed,  clear  that  the  more  the  superficial  fibres  are  developed  the  greater  must 
be  the  traction  exerted  on  the  choroid,  and  this  traction  has  evidently  for  its  object  the  protection  of 
the  sclera  against  the  increase  of  tension  during  accommodation.  If  the  posterior  extremity  of  the 
muscle  were  fixed,  the  sclera  would  be  exposed  to  this  tension  every  time  one  would  accommodate.  In 
view  of  this  relation,  it  may  be  interesting  to  observe  that  the  eye  which  I  examined,  in  which  the  an- 
terior surface  of  the  crystalline  lens  did  not  advance  during  accommodation,  is  myopic  about  6  D.,  and 
that  that  one  of  the  three  eyes  of  Helmholtz  which  showed  the  least  advancement  was  slightly  myopic. 


188  PHYSIOLOGIC  OPTICS 

illusion.  Holding  the  crystalline  lens  of  a  horse  in  front  of  a  red 
ground  we  see  this  color  through  the  whole  crystalline  lens,  except  at  a 
quite  narrow  border  where  the  red  rays  undergo  total  reflection.  By 
exerting  a  traction  on  the  zonula,  this  border  enlarges  at  the  expense 
of  the  transparent  part,  which  makes  one  think  of  a  diminution  of  the 
diameter  of  the  crystalline  lens. 

We  have  not  succeeded,  up  to  the  present,  in  explaining  satisfactorily 
the  singular  phenomena  which  I  observed  when  the  accommodation 
attained  its  maximum  (page  180).  I  had  attributed  them  to  a  displace- 
ment downwards  of  the  crystalline  lens,  due  to  an  unequal  traction  on 
the  zonula.  But  since  Hess  and  Heine  have  shown  that  the  displacement 
takes  place  following  the  weight,  this  explanation  must  of  necessity  be 
abandoned.  Hess  supposes  that  the  crystalline  lens  falls  downwards 
by  the  relaxation  of  the  zonula,  as  stated  by  Helmholts,  but  apart  from 
the  fact  that  the  hypothesis  of  Helmholtz  must  be  rejected  for  other 
reasons,  it  is  not  easy  to  any  longer  suppose,  in  view  of  the  manner  in 
which  the  crystalline  lens  is  fixed  on  the  vitreous  body,  that  it  can  fall 
downwards  unless  the  anterior  part  of  the  vitreous  body  is  displaced 
also.  The  fact  that  the  movement  of  the  small  image  is  much  wider 
than  that  of  the  large  one  (i),  indicates  in  every  case  that  there  can  be 
no  question  of  a  displacement  directly  downwards,  but  rather  a  see-saw 
movement  downwards  and  backwards.  —  Among  other  explanations 
which  might  occur  to  us,  that  of  a  deformity  due  to  a  displacement  of 
the  crystalline  mass  in  the  interior  of  the  capsule  would  perhaps  be  the 
most  probable. 

As  to  the  contraction  of  the  pupil  which  accompanies  accommodation, 
it  is  evident  that  it  has  the  effect  of  eliminating  the  peripheral  parts  of 
the  crystalline  lens,  which,  by  reason  of  their  flattening,  would  render 
the  image  too  poor.  We  know  also  that  when  the  pupil  is  dilated  with 
an  alkaloid  which  has  little  or  no  effect  on  the  accommodation  (cocaine 
or  homatropine),  near  sight  diminishes  relatively  more  than  far  sight; 
this  phenomenon  is  often  attributed  to  a  diminution  of  the  amplitude 
of  accommodation,  but  at  least  with  cocaine  I  have  only  very  rarely 
been  able  to  prove  a  real  diminution  of  this  amplitude.  We  must  note, 
however,  that  eyes  which  have  a  strong  spherical  aberration  correct  this 
aberration  by  accommodation ;  these  eyes  may,  therefore,  see  relatively 
better  near  at  hand  than  far  away,  when  the  pupil  is  dilated. 

(1)  A  slight  displacement  of  the  look  downwards  would  give  analogous  phenomena.  When  the  eye 
makes  a  movement,  the  displacement  of  the  images  is  in  direct  relation  with  the  distance  of  the  center 
of  curvature  of  the  surface  in  question  to  the  center  of  rotation  of  the  eye.  The  displacement  of  the 
small  image  is  relatively  large  because  the  center  of  curvature  of  the  posterior  surface  of  the  crystalline 
lens  is  situated  very  far  forward  in  the  eye. 


ACCOMMODATION  189 

When,  in  a  paracentesis,  we  allow  the  aqueous  humor  to  escape,  we 
know  that  the  crystalline  lens  and  the  iris  come  to  be  applied  against 
the  cornea,  without  this  membrane  noticeably  changing  form.  In  all 
probability,  the  crystalline  lens  is  then  in  the  state  of  highest  accommo- 
dation, because  it  could  not  make  such  a  movement  without  exerting 
a  strong  traction  on  the  zonula.  While  performing  paracentesis  on  a 
rabbit's  eye,  Mannhardt  claims  that  he  saw  also  the  accommodative 
displacement  of  the  images  of  Purkinje,  by  means  of  the  ophthalmoscope 
of  Cramer.  It  becomes  probable,  therefore,  that  the  pupillary  contrac- 
tion, which  accompanies  the  escape  of  the  aqueous  humor,  is  accom- 
modative. But  the  pupillary  contraction  accompanies  the  escape  of"  the 
aqueous  humor  even  in  a  dead  eye ;  by  introducing  the  point  of  a  Pravas 
syringe  into  the  anterior  chamber,  it  is  easy  to  dilate  or  contract  the 
pupil  at  will  by  injecting  or  removing  the  liquid.  This  contraction  is, 
therefore,  purely  mechanical,  and  it  then  becomes  probable  that  the 
accommodative  contraction  of  the  pupil  is  so  also,  although  this  mech- 
anism is  not  yet  clearly  elucidated. 

Bibliography.  —  Petit  (J.  L.).  Memoire  «ur  le  crynfallin  de  VceH  de  Fhomme.  Hist,  de 
1'  Academie  des  Sciences,  1730.  —  Krause  (C.).  Poggendorfs  Annalen,  1834-36.  —  Max  Lan- 
genbeck.  Klinische  Beitrdge  zur  Chirurgie  und  Ophthalmohgif.  Gottingen,  1849.  —  Cramer 
(A.).  Het  Accommodatievermogen  der  Oogen.  Haarlem,  1853.  Translated  into  German  by 
Doden.  Leer,  1855.  —  Helmholtz  (H.).  Ueber  die  Accommodation  des  Avges.  Archiv  fiir 
Ophtalmologie,  I,  2.  —  Griife  (A.).v.  Fall  von  acquirirter  Aniridie  ah  Btitrag  zur  Accommoda, 
tionslehre.  A.  f.  O.  VI F,  2.  p.  150.  —  Briicke  (E.).  Anatomixche  Beschreibung  des  menschlichen 
Augapfels.  Berlin,  1847.  —  Bowman  (William).  Lectures  delivered  in  the  London  Royal  oph- 
thalmic hospital  Moorfields,  1847.  —  Miiller  (Heinrich).  Ueber  einen  ringfb'rmigen  Muskel 
am  Ciliarkorper  des  Menschen  und  ilber  den  Mechanismus  der  Accommodation.  A.  f.  O.,  Ill,  p.  1. 
—  Mannhardt.  Bemerkungen  ilber  d(n  Accommodationsmuskel  und  die  Accommodation.  Arch, 
fur  Opht.,  IV,  1.  —  Hueck  (A.).  Die  Bewegung  der  Krystattinse.  Leipzig,  1841.  —  Coccius 
(A.).  Ueber  den  Mechanismus  der  Accommodation  des  menschlichen  Auges.  Leipzig,  1867.  — 
Forster  (R. ).  Zur  Kenntniss  der  Accommodafionsmechanismus.  Kl.  M.  f.  A.,  1864  p.  368.  — 
Rochon-Duvignaud.  Recherches  sur  F  angle  de  la  chambre  anterieure  et  le  canal  de  Schlemm, 
Paris,  Steinheil,  1892.  —  Tscherning  (M. ).  Etude  sur  le  mecanisme  de  V accommodation.  Arch,  de 
phys.,  January,  1894.  —  L'optometi-e  de  Young  et  son  emploi.  Arch,  de  phys.,  October,  1894.  — 
Recherches  sur  les  changements  optiques  de  I'ceil  pendant  1J accommodation.  Arch,  dephys.,  Janu- 
ary, 1895.  —  Theorie  des  changements  optiques  de  I'ceil  pendant  F  accommodation.  Arch,  de  phys. 
January,  1895.  — Crzellitzer  (A.).  Die  Tscherningsche  Accommodativnstheorie.  Grafe's  Ar- 
•chiv,  XLII,  4,  1896.  — Stadfeldt  (A.).  Die  Veranderung  der  Lime  bei  fraction  der  Zonula. 
Kl.  M.  f.  A.,  December,  1896.  —  Crzellitzer  (A.).  Zonularspannung und Linsenform.  Bericht 
der  Heidelberger  Gesellschaft,  1896.  —  He?s  (C.).  Arbeiten  aus  dem  Gebiete  der  Accommoda- 
tionslehre.  Grafe's  Archiv,  1896-99. — Heine  (L.).  Die  accommodation  Linsenverschiebungen 
im  Auge.  Grafe's  Archiv,  1897.  — Tscherning  (M.).  The  Theory  of  Accommodation.  Oph- 
thalmic Review,  April,  1899.  —  Tscherning  (M.).  La  surcorrection  accommodative  de  Vaber- 
ration  de  sphericite  de  I' ceil.  Journal  de  Physiologic,  March,  1899. 


CHAPTER  XIII. 

OPHTHALMOSCOPY. 

88.  Methods  of  Illuminating  the  Fundus  of  the  Eye.  —  It  has  been 
known  from  the  remotest  times  that  the  pupil  of  certain  animals  (dog, 
cat,  etc.)  can  appear  luminous.  The  phenomenon  was  thought  to  be 
analogous  to  the  production  of  light  by  the  glow-worm  (phosphorescence) ; 
in  reality  it  is  due  to  the  existence  of  the  tapetum,  a  part  of  the  choroid 
the  retinal  surface  of  which  is  strongly  reflecting  and  has  a  metallic 
reflex :  its  purpose  is  not  very  well  elucidated.  As  to  the  human  pupil, 
it  has  been  known  for  a  long  time  that  it  may,  in  very  rare  cases,  appear 
luminous  after  the  development  of  an  interior  tumor  of  the  eye  (amaurotic 
cat's-eye).  Beer  also  remarked  the  ocular  glow  in  certain  cases  of  aniridia. 

Towards  1850  dimming  and  Bruecke  discovered  the  method  of  making 
the  pupil  of  the  normal  eye  appear  luminous,  and  Hclmholtz  in  1851 
achieved  the  great  invention  of  the  ophthalmoscope  which  was  destined 
to  revolutionize  ophthalmology. 

Like  every  other  object  the  fundus  of  the  eye  sends  back  light  when 
it  is  illuminated.  Let  A  (fig.  125)  be  a  luminous  point  for  which  the 


Fig.  125. 

eye  is  accommodated.  This  point  sends  into  the  eye  the  cone  ABC, 
the  rays  of  which  reunite  at  D.  This  point,  being  illuminated,  sends  the 
rays  in  all  directions;  those  contained  in  the  cone  ABC  emerge  from 
the  eye  to  meet  at  a  point  A.  Generally,  therefore,  the  eye  can  send 
back  light  to  a  point  which  has  first  sent  the  light  to  it,  and  if  in  ordinary 
circumstances  the  pupil  of  the  eye  appears  black,  it  is  because  the  pupil 

190 


OPHTHALMOSCOPY  191 

of  the  observing  eye,  being  black,  cannot  send  light  back  into  the  ob- 
served eye.  In  order  that  it  may  appear  luminous,  a  luminous  source 
must  be  placed  in  front  of  the  observing  eye;  this  is  what  we  do  by 
means  of  the  ophthalmoscope. 

Following  are  the  different  circumstances  in  which  we  can  see  the 
pupil  luminous : 

a.  The  pupil  of  albinos  is  seen  red  because  the  fundus  of  the  eye  is 
illuminated  by  the  light  which  has  passed  through  the  sclera.     If  we 
cover  the  eye  with  a  screen  pierced  by  an  aperture  corresponding  to 
the  pupil,  the  latter  appears  black.  —  By  concentrating  a  bright  light 
on  the  sclera  by  means  of  a  lens,  we  can  make  the  pupil  of  a  normal 
eye  luminous,  especially  if  the  person  has  a  fair  complexion. 

b.  If,  in  the  case  of  figure  125,  the  eye  is  not  exactly  focused  for  the 
luminous  point,  the  latter  illuminates  on  the  retina  a  circle  of  diffusion 
(ab,  fig.  126).    This  circle  sends  back  the  light  not  only  in  the  direction 


Fig.  126. 

of  the  luminous  point,  but  also  in  neighboring  directions :  thus  the  point 
a  sends  back  the  cone  BaC  which,  outside  the  eye,  takes  the  direction 
ABCd,  so  that  the  observing  eye  o  may  be  placed  in  this  cone.  Placing 
a  lamp  at  some  distance  from  the  observed  eye  and  sighting  near  the 
border  of  the  flame,  from  which  we  shelter  ourselves  by  a  screen,  we 
can  frequently  see  the  pupil  luminous,  especially  if  it  is  a  little  large 
and  if  the  patient  does  not  fix  the  flame. 

The  experiment  succeeds  more  easily  if  the  observed  eye  is  strongly 
ametropic,  because  then  the  rays,  having  emerged  from  the  eye,  soon 
diverge  greatly,  so  that  the  observing  eye  may  easily  find  a  place  in  the 
luminous  cone.  If  the  eye  is  not  ametropic  we  can  make  it  so  by  means 
of  a  strong  lens  or  by  putting  it  under  water,  or,  as  Bellarminoff  has 
lately  done,  by  placing  a  plate  of  glass  in  contact  with  the  cornea  so  as 
to  eliminate  the  refracting  power  of  this  membrane.  By  this  latter 
means  we  can  make  the  fundus  of  the  eye  visible  for  several  persons  at 
once.  —  In  the  case  of  amaitrotic  cat's-eye,  the  presence  of  the  tumor  in 
the  interior  of  the  eye  makes  the  latter  strongly  hypermetropic,  so  that 
the  fundus  becomes  easily  visible. 


192 


PHYSIOLOGIC   OPTICS 


c.  PRINCIPLE  OF  THE  OPHTHALMOSCOPE  OF  HELMHOLTZ.  —  Let  AB 
(fig.  127)  be  a  plate  of  plane,  parallel  glass  and  L  a  lamp  which  sends 
light  towards  this  plate.  The  greater  part  of  the  light  passes  through 
the  plate,  but  a  part  is  reflected  towards  the  observed  eye,  D.  It  enters 
this  eye  and  illuminates  the  retina.  The  latter  sends  back  light  towards 
the  plate :  a  part  of  this  light  is  reflected  towards  the  lamp  L,  but  the 
greater  part  passes  through  the  plate  and  enters  the  observing  eye  C, 
which,  consequently,  sees  luminous  the  pupil  of  the  observed  eye.  To 


Fig.  127.  —  Principle  of  the  ophthalmoscope  of  Hdmholtz. 


compensate  for  the  loss  of  light  which,  proceeding  from  L,  passes 
through  the  plate,  Helmholts  used  several  plates,  placed  one  behind  the 
other. 

d.  PRINCIPLE  OF  THE  ORDINARY  OPHTHALMOSCOPE.  —  We  obtain  a 
more  intense  illumination  by  means  of  a  silvered  mirror;  the  observer 
looks  through  a  small  portion  from  which  the  coating  has  been  removed 
or  which  has  been  perforated.  —  As  a  concave  mirror  concentrates  the 
light  it  illuminates  better  than  a  plane  mirror,  and  the  latter  better  than 
a  convex  mirror,  (i)  Generally  it  is  useful  to  have  a  good  illumination ; 
but  we  sometimes  see  better  the  very  delicate  changes  in  the  fundus  of 
the  eye  by  using  a  weak  illumination,  and  very  delicate  opacities  of  the 


(1)  The  clearness  of  the  retinal  image  of  the  flame  which  is  formed  in  the  observed  eye  is  the  same 
in  all  cases,  but  the  image  is  larger  when  we  use  a  concave  mirror  than  when  we  use  a  plain  or  convex 
mirror.  —  One  can  verify  this  for  oneself  by  putting  one's  eye  in  the  place  of  the  observed  eye.  The 
image  of  the  flame  which  one  then  sees  in  the  mirror  corresponds  to  the  illuminated  part  of  the  retina ; 
it  is  larger  in  the  case  of  the  concave  mirror  than  with  the  plane  or  convex  mirror.— Placing  the  flame 
behind  the  mirror,  one  sees,  in  the  same  circumstances,  the  opening  as  a  luminous  circle  which  cor- 
responds to  the  part  of  the  fundus  of  the  eye  which  the  observer  can  see  at  once  (ophthalmoscopic 
field). 


OPHTHALMOSCOPY  193 

vitreous  body  or  of  the  crystalline  lens  disappear  if  the  illumination  is 
too  strong. 

The  ophthalmoscope  is  the  only  practical  means  of  illuminating  the 
eye.  Nevertheless,  a  different  method  may  sometimes  prove  service- 
able. We  place  the  lamp  behind  the  observer  so  that  the  light  reaches  the 
observed  eye  by  glancing  along  the  head  of  the  observer;  we  concen- 
trate the  light  on  the  eye  with  a  lens.  When  the  pupil  is  dilated  we  can 
thus  see  the  fundus  of  the  eye  feebly  illuminated,  and  we  often  dis- 
tinguish very  distinctly  details  situated  far  forward  in  the  vitreous  body 
(tumors  of  the  ciliary  body,  detachments,  etc.). 

89.  Examination  by  the  Erect  Image  (Helmholtz).  —  The  conditions  for 
seeing  the  pupil  luminous  were  known,  before  Helmholte,  by  the  re- 
searches of  Gumming  and  Brucckc,  and  Babbage  seems  to  have  already 
illuminated  the  pupil  with  a  mirror  from  a  small  portion  of  which  the 
coating  was  removed  for  observation  purposes;  but  none  of  these 
scientists  thought  of  studying  the  conditions  under  which  this  ocular 
glow  can  form  an  image  of  the  fundus  of  the  eye. 

When  preparing  the  lectures,  in  the  course  of  which  he  was  to  illus- 
trate for  his  class  the  methods  of  making  the  pupil  appear  luminous, 
Helmholtz  proposed  to  himself  the  problem  to  be  solved,  not  a  difficult 
task  for  an  experienced  physicist.  He  easily  succeeded  in  solving  it 
theoretically,  and  then  constructed  the  first  ophthalmoscope  by  com- 
bining some  glass  plates  with  the  lenses  of  a  test  case ;  after  some  days 
of  hard  work  he  succeeded  in  seeing  the  fundus  of  the  living  eye  which 
no  one  had  ever  seen  before  him. 

Helmholtz  used  examination  by  the  erect  image.  Suppose  that  the 
observer  is  emmetropic  (if  he  is  not  he  must  correct  his  refraction) :  he 
can  then  see  the  fundus  of  the  eye  of  another  emmetrope  without  any 
further  aid,  since  the  rays  emerging  from  the  observed  eye  are  parallel. 
If  the  observed  person  is  not  emmetropic  he  must  be  made  emmetropic. 
We,  therefore,  look  for  the  strongest  convex  glass  or  the  weakest  con- 
cave glass  with  which  we  can  see  the  fundus  of  the  eye  distinctly:  this 
glass  indicates  at  the  same  time  the  refraction  of  the  eye ;  but  the  ob- 
server must  cultivate  the  habit  of  not  using  his  accommodation,  other- 
wise the  results  will  be  false.  —  The  refraction  which  we  find  with  the 
ophthalmoscope  ought  to  be  in  agreement  with  that  found  by  subjective 
examination.  It  must  be  noted,  however,  that  the  glass  of  the  ophthal- 
moscope is  generally  a  little  farther  away  from  the  eye  examined  than  a 
glass  placed  in  a  frame.  We  find  therefore,  as  by  the  subjective  method, 


194  PHYSIOLOGIC  OPTICS 

too  low  a  number  for  hypermetropia,  too  high  a  number  for  myopia, 
and  the  error  is  more  pronounced  in  the  case  of  an  ophthalmoscopic 
examination  on  account  of  the  greater  distance.  For  low  degrees  of 
ametropia  it  is  insignificant;  for  high  degrees,  especially  of  myopia,  it 
is  sufficient  to  make  the  determination  fallacious.  Latent  hypermetropia 
is  generally  disclosed  by  ophthalmoscopic  examination  because  in  the 
dark  room  the  patients  do  not  fix. 

MAGNIFICATION.  —  To  obtain  a  numerical  expression  of  ophthalmo- 
scopic magnification,  we  may  compare  the  retinal  image,  formed  in  the 
observing  eye,  of  an  object  (the  papilla  of  the  fundus  of  the  examined 
eye)  with  the  retinal  image  which  the  observing  eye  would  have  of  the 
same  object,  placed  free  in  air,  at  the  working  distance  of  the  observer. 
We  often  make  this  distance  20  centimeters. 

Let  us  suppose  that  both  eyes,  that  of  the  observer  and  that  of  the 
observed  person,  are  emmetropic. 

Let  O  =  AB  (fig.  128)  be  the  object  of  the  fundus  of  the  observed 
eye ;  we  draw  the  rays  AC  and  BD  parallel  to  the  axis.  These  two  rays 
will  intersect  at  the  anterior  focus  3^,  and  all  the  other  rays  proceeding 


Patient 


Fig.  128. 


Observer 


from  A  and  B  are  parallel  to  either  of  these ;  among  other  rays  ^E  and 
4>\G  which,  prolonged,  pass  through  the  anterior  focus  of  the  observing 
eye.  After  refraction  in  this  eye  these  rays  are  parallel  and  determine 
the  size  of  the  image,  I.  Designating  by  F±  the  anterior  focal  distance 
of  the  observed  eye,  by  F\  that  of  the  observing  eye,  the  two  similar 
triangles  CD4>X  and  EG4>\  give  the  relation : 

JL        F/i 
O  F!  ' 

We  see  that,  if  the  optic  systems  of  both  eyes  are  alike,  I  is  equal  to  O. 
The  papilla  of  the  observed  eye  forms  in  the  observing  eye  an  Image 
equal  to  itself.  By  placing  the  fundus  of  the  eye  free  in  the  air  at  the 


OPHTHALMOSCOPE 


195 


working  distance,  equal  to  20  centimeters,  the  retinal  image  Ij  of  the 
object  O  (fig.  129)  would  be  found  by  the  formula 


200 


By  multiplying  this  formula  by  the  preceding  one,  we  obtain  the 
magnification  in  the  erect  image  : 


200mm 


By  supposing  15  millimeters  for  Fa,  the  magnification  would  be  about 
13,  but  this  number  is  arbitrary,  since  the  working  distance  has  been 
chosen  arbitrarily. 


Fig.  129. 


Observer 


If  the  observed  eye  is  myopic,  the  magnification  is  greater,  supposing 
that  the  correcting  glass  is  beyond  the  anterior  focus  of  the  observed 
eye,  as  is  always  the  case.  The  construction  is  the  same  as  in  the  pre- 
ceding case,  but  on  meeting  the  concave  glass  the  rays  C^  and  D<^t  (fig. 
130)  are  made  more  divergent.  The  rays  ^E  and  &\G  which  are 


Patient 


Fig.  180. 


Observer 


parallel  to  them  diverge,  therefore,  more  than  in  the  preceding  case, 
which  makes  the  image  Ix  greater.    If  there  is  a  case  of  a  myopia  of 


19C  PHYSIOLOGIC  OPTICS 

curvature  the  magnification  is  still  greater;  the  point  4^  is,  in  fact, 
situated  nearer  the  observed  eye,  which  causes  the  rays  HK  and  LM, 
and  consequently  also  the  rays  ^E  and  ^G  to  diverge  still  more.  In 
the  hypermetropic  eye  the  reverse  takes  place.  It  follows  that  in  an 
astigmatic  eye  we  see  the  papilla  elongated  in  the  direction  of  the  meri- 
dian of  greatest  refraction. 

OPHTHALMOSCOPIC  FIELD.  —  According  to  Helmholtz  we  find  the 
ophthalmoscopic  field,  that  is  to  say,  the  aggregate  of  the  parts  of  the 
fundus  of  the  eye,  visible  simultaneously  by  joining  by  straight  lines 
the  middle  of  the  pupil  of  the  observing  eye  to  the  borders  of  the  pupil 
of  the  observed  eye,  and  by  making  these  straight  lines  undergo  the 
same  refraction  in  the  observed  eye  as  if  they  were  rays.  Figure  131 
shows  that  the  field  is  greater  in  the  hypermetropic  eye,  smaller  in  the 
myopic  eye,  if  the  observing  eye  is  beyond  the  anterior  focus  of  the 
observed  eye,  as  is  always  the  case.  As  it  is  the  border  of  the  pupil  of 
the  observed  eye  which  limits  the  field,  we  increase  it  by  instilling 
atropine. 


Patient  Observer 

Fig.  131.  —  Construction  of  the  ophthalmoscopic  field. 

This  is  an  instance  of  inverse  constructions  which  we  frequently  use 
in  geometric  optics;  to  know  what  points  of  the  fundus  of  the  ob- 
served eye  can  send  back  rays  into  the  pupil  of  the  observing  eye,  we 
reverse  the  problem  by  imagining  the  pupil  of  the  observing  eye  lumin- 
ous and  finding  what  parts  of  the  fundus  of  the  observed  eye  it  can 
illuminate.  The  result  is  the  same  on  account  of  the  reversibility  of  the 
optic  processes.  In  reality  the  field  is  a  little  larger  than  that  which  we 
have  found  by  our  construction,  since  we  have  reduced  the  pupil  of  the 
observing  eye  to  a  point;  from -the  point  d,  situated  outside  the  field, 
some  rays  could  still  enter  the  observing  eye  through  the  lower  parts  of 
the  pupil.  To  have  the  field  complete  it  would  be  necessary  to  construct, 
not  the  image  pi  of  the  center  of  the  pupil  p,  but  the  image  of  the  entire 
pupil  or  rather  of  the  opening  of  the  ophthalmoscope,  formed  by  the 


OPHTHALMOSCOPY  197 

optic  system  of  the  observed  eye.    We  would  thus  obtain  a  larger  field, 
but  the  parts  near  the  border  would  be  very  slightly  illuminated. 

90.  Examination  by  the  Erect  Image.  Observations.  —  To  tell  the  size 
of  intra-ocular  objects,  it  is  customary  to  compare  them  with  the  dia- 
meter of  the  papilla;  we  thus  say  that  the  width  of  a  staphyloma  is  the 
fourth  or  half  of  the  diameter  of  the  papilla.  The  attempts  which  have 
been  made  to  obtain  more  exact  measurements  by  means  of  a  micro- 
meter (Bonders,  Lcroy)  have  not  given  practical  results. 

The  refraction  is  usually  the  same  for  the  entire  fundus  of  the  eye. 
According  to  Young,  if  we  suppose  a  sphere  drawn  around  the  eye  with 
the  distance  of  the  far  point  as  radius,  the  position  of  the  retina  is  such 
that  it  is  everywhere  found  at  the  place  where  the  best  images  of  objects 
situated  on  this  sphere  would  be  formed.  A  certain  degree  of  astigma- 
tism by  incidence  is  inevitable  for  the  peripheral  parts;  but  the  retina 
is  here  found  between  the  two  focal  lines  almost  at  the  place  which 
would  correspond  with  the  circular  diffusion  spot. 

Thanks  to  this  arrangement,  we  can  use  the  papilla  for  the  determina- 
tion of  refraction  by  the  erect  image;  generally  its  refraction  scarcely 
differs  from  that  of  the  macula.  There  are  exceptions  to  this  rule,  how- 
ever. For  instance,  I  examined  on  consultation  a  young  man  in  whom 
a  myopia  of  4  D.  was  indicated,  while  a  colleague,  very  experienced  in 
determination  by  the  erect  image,  and  myself  found,  each  for  himself, 
emmetropia  by  the  ophthalmoscope.  It  was  later  established  beyond 
doubt  that  the  patient  had  really  a  myopia  of  4  D.  Then,  asking  our- 
selves whether  the  myopia  might  not  be  due  to  a  spasm  of  accommo- 
dation, we  resorted  to  a  treatment  by  atropine,  but  without  changing 
the  result.  Analogous  differences  seem  quite  frequent  in  cases  of  ex- 
cessive myopia,  by  reason  of  the  elongated  form  of  the  globe. 

A  difference  between  subjective  and  ophthalmoscopic  refraction  may 
therefore  be  due:  i°  to  a  greater  distance  of  the  correcting  glass  from 
the  observed  eye  (see  page  194) ;  2°  to  the  fact  that  a  latent  hyperme- 
tropia  may  become  manifest  in  the  darkness ;  3°  to  the  fact  that  the 
papilla  may  have  a  different  refraction  from  the  macula ;  4°  to  simulation. 

To  judge  of  the  depth  of  a  papillary  excavation  we  can  measure  the 
difference  of  refraction  between  the  edge  and  pit  of  the  excavation, 
keeping  in  mind  that  a  difference  of  one  dioptry  corresponds  to  almost 
a  third  of  a  millimeter.  We  can  measure  by  the  same  process  the  tume- 
faction of  the  papilla  in  cases  of  optic  neuritis,  the  distance  of  an  opacity 
of  the  vitreous  body  from  the  retina,  etc. 


198  PHYSIOLOGIC  OPTICS 

Another  means  of  judging  whether  one  point  is  situated  in  front  of 
another  consists  in  making  slight  movements  of  the  head  (with  the 
ophthalmoscope).  We  shall  then  see  the  nearer  point  make  a  move- 
ment in  a  contrary  direction  in  relation  to  the  other  point  (parallax). 

The  magnification  of  13  which  we  have  found  for  the  erect  image 
has  nothing  to  do  with  the  apparent  size  of  the  papilla,  which  depends 
on  the  distance  to  which  we  project  the  image  without  knowing  it. 
When  we  begin  to  use  the  ophthalmoscope,  the  papilla  frequently  ap- 
pears very  small,  and  generally  its  size  seems  to  vary  for  different  ob- 
servers. I  have  noticed  a  phenomenon  of  the  same  kind  when  looking 
at  a  luminous  point  (see  page  138).  If  the  point  is  very  distant  the 
circle  of  diffusion  appears  very  large  to  me.  But  if  I  observe  a  luminous 
point  placed  at  the  focus  of  a  lens  of  20  D.,  held  in  front  of  my  eye,  the 
point  appears  extremely  small,  and  this  although  the  retinal  image  ought 
to  be  exactly  the  same  in  both  cases.  Accommodation  is  often  charged 
with  playing  a  part  in  this  optic  illusion,  but  we  must  observe  that  it 
takes  place  even  if  every  trace  of  accommodation  be  excluded.  It  rests 
on  an  unconscious  conclusion  relatively  to  the  distance  of  the  object  (see 
chapter  XXII). 

The  macula  is  usually  difficult  to  see :  most  frequently  the  pupil  must 
be  dilated.  The  fovea  is  sometimes  visible  as  a  dark  spot  with  a  small 
whitish  point  in  the  middle;  its  place  is  marked  in  every  case  by  the 
peculiar  manner  in  which  the  vessels  come  from  all  sides  to  disappear 
in  its  vicinity.  We  never  see  a  trace  of  the  yellow  color  which  is  so 
striking  in  the  dead  eye ;  certain  authors  have,  therefore,  considered  this 
yellow  coloration  as  a  phenomenon  due  to  changes  after  death,  and  this 
idea  seems  confirmed  by  an  observation  which  I  have  made.  We  gen- 
erally suppose  that  if  we  do  not  see  the  yellow  color  of  the  macula,  it 
is  because  the  yellow  light  is  drowned  by  the  red  light  reflected  by  the 
blood.  I,  therefore,  thought  that  we  should  be  able  to  see  it  by  illumi- 
nating the  eye  with  a  strong  sodium  flame.  The  blood  does  not  reflect 
this  light  or  reflects  it  only  slightly,  and  the  appearance  of  the  fundus 
of  the  eye  recalls  that  of  photographic  illustrations  of  ophthalmoscopic 
images;  we  see  the  vessels  black  on  a  gray  ground,  but  the  macula, 
which  we  should  expect  to  find  illuminated,  remains  at  least  as  dark  as 
in  ordinary  ophthalmoscopy. 

The  red  color  of  the  fundus  of  the  eye  is  due  to  the  vessels  of  the 
choroid ;  wherever  the  choroid  is  defective  we  see  the  white  background 
of  the  sclera,  in  cases  of  coloboma  for  example.  It  is  curious  that  we 
never  see  a  trace  of  the  retinal  purple  with  the  ophthalmoscope.  In  the 


OPHTHALMOSCOPY  199 

normal  state  the  retina  is  completely  transparent ;  we  see  only  its  vessels. 
Sometimes  we  can,  however,  distinguish  it  as  a  grayish  veil  in  the  parts 
near  the  papilla.  If  the  black  pigment  be  strongly  developed,  the  fundus 
of  the  eye  appears  of  a  uniform  deep  red.  If  it  is  but  slightly  developed, 
the  fundus  has  often  a  marble  or  spotted  appearance  due  to  the  meshes 
of  the  vascular  network  of  the  choroid. 

Most  normal  eyes  have  a  physiologic  excavation  or  cup  of  the  papilla 
which  has  the  appearance  of  a  whitish  spot.  It  is  then  easy  to  see, 
by  the  erect  image,  that  the  bottom  is  more  myopic  than  the  border; 
we  see  indistinctly  the  vessels  of  the  excavation  when  those  of  the 
borders  appear  distinct  and  vice  versa,  at  least  when  the  excavation  is 
a  little  deep.  The  physiologic  cup  never  reaches  the  borders  of  the 
papilla.  We  can  be  certain  that  an  excavation  is  pathologic  only  when 
it  reaches  the  borders  everywhere. 

We  frequently  perceive  in  the  normal  eye  a  pulsation  of  one  or  several 
of  the  large  veins.  During  the  systole  the  tension  of  the  globe  increases 
enough  to  compress  the  large  veins  near  their  starting  place  where  the 
intra-venous  tension  is  weakest.  At  the  moment  of  diastole  the  tension 
of  the  globe  diminishes,  the  pressure  ceases  and  the  veins  empty  them- 
selves, (i) 

The  pulsation  of  the  arteries  is  nearly  always  a  sign  of  glaucoma ;  the 
tension  of  the  globe  is  so  high  that  the  arteries  remain  empty,  except 
at  the  moment  of  systole. 

The  papilla  is  generally  limited  by  a  very  thin  white  border,  some- 
times surrounded  by  an  incomplete  black  border,  formed  by  the  pigment 
of  the  choroid.  The  white  border  is  called  the  scleral  border;  it  is 
attributed  to  the  visibility  of  the  sclera  between  the  choroid  and  the 
papilla.  Sometimes  it  is  larger  and  mistaken  for  an  incipient  staphyloma. 

One  can  see  the  red  fundus  of  one's  own  eye  by  looking  in  a  mirror 
held  before  a  flame.  A  luminous  pencil  passes  through  the  opening  of 
the  ophthalmoscope,  enters  the  eye,  is  reflected  by  the  retina,  emerges 
from  the  eye,  meets  the  mirror,  and  is  again  reflected  towards  the 
retina.  If  the  course  of  the  rays  permit,  for  example  if  the  eye  is  emme- 
tropic  and  the  mirror  plane,  we  may  even  distinguish  the  details.  We 

(1)  [Lately  Dr.  S.  Turk  has  studied  this  question  again  in  a  number  of  persons  with  irregular  heart- 
beat (arythmia). 

These  observations  prove  that  the  venous  narrowing  is  independent  of  the  entrance  of  the  arterial 
pulse  wave  into  the  eye,  and  he  infers  that  the  cardiac  systole  produces  not  the  narrowing,  but  the  dila- 
tation of  the  veins.  He  further  shows  that  this  venous  pulsation  cannot  be  caused  by  a  rhythmic  inter- 
ference with  the  exit  of  the  blood  from  the  vena  centralis  retinee  because  a  dilatation,  caused  in  this 
way,  ought  to  be  propagated  opposite  to  the  direction  of  the  blood-current.  He,  therefore,  considers  this 
phenomenon  caused  by  a  propagation  of  the  arterial  pulse  wave  through  the  capillaries  into  the  veins 
which  is  accounted  for  by  the  relatively  high  extravascular  pressure  in  the  eye  (Engelmann'sArch.f. 
Physiol.,1899).]  —  W. 


200  PHYSIOLOGIC  OPTICS 

see  at  the  same  time  the  catoptric  image  of  the  cornea  as  a  large  circle 
of  diffusion. 

Auto-ophthalmoscopes  have  been  constructed  as  well  as  ophthalmo- 
scopes, by  means  of  which  several  observers  can  see  simultaneously  the 
fundus  of  the  eye. 

Another  way  of  examining  oneself  consists  in  observing  with  one  eye 
the  image  of  the  other  formed  by  a  looking-glass;  we  can  in  this  way 
perform  ophthalmoscopy  of  the  left  eye  with  the  right  eye  by  the  in- 
verted image,  and  we  can,  with  a  small  concave  mirror  placed  not  far 
from  the  eye,  observe  the  images  of  Purkinje,  etc.  It  was  by  working 
thus  with  my  own  eye  that  I  observed  for  the  first  time  the  conical 
deformity  of  the  anterior  surface  of  the  crystalline  lens  during  accom- 
modation (page  176). 

91.  Examination  by  the  Inverted  Image.  —  This  examination  was  in- 
troduced into  oculistic  practice  by  Ruete  in  1852.  It  was  especially 
adopted  and  developed  by  the  Berlin  school  (Graefe),  while  the  Vienna 
school  (Jaeger)  especially  used  the  erect  image.  As  the  Berlin  school 
held  for  a  long  time  a  more  influential  position,  examination  by  the  in- 
verted image  was  for  a  long  time  more  used  than  the  other.  The  two 
methods,  however,  merit  a  place  side  by  side.  The  inverted  image  gives 
a  less  magnification  and  a  larger  field:  it  is,  therefore,  very  useful  for 
studying  the  general  appearance  of  the  fundus  of  the  eye,  while  the  erect 
image  serves  especially  for  the  study  of  the  details  and  for  the  determina- 
tion of  refraction. 

Examination  by  the  inverted  image  is  made  by  holding  a  strong 
convex  lens  (most  frequently  -f-  13)  at  a  distance  from  the  eye  almost 
equal  to  its  focal  distance.  This  lens  forms  a  real  and  inverted  image  of 
the  fundus  of  the  eye,  situated  on  the  other  side  of  the  iens,  in  the 
vicinity  of  its  second  focus.  It  is  this  image  that  the  observing  eye  sees 
when  accommodating,  or,  which  is  better,  by  looking  through  a  convex 
lens  of  about  4  D.,  placed  behind  the  mirror.  If  the  examined  eye  is 
emmetropic,  the  rays  leaving  the  eye  are  parallel  and  the  image  is 
formed  at  the  focus  of  the  lens ;  if  it  is  myopic  the  image  is  a  little  nearer, 
if  hypermetropic  a  little  farther  than  the  focus.  In  the  latter  case  the 
observer  is  frequently  obliged  to  move  back  a  little  in  order  to  see  the 
image  distinctly. 

MAGNIFICATION.  —  If  we  use  a  lens  of  +  13,  the  magnification  is 
about  five  times  for  an  emmetropic  eye.  Let  ab  =  O  (fig.  132)  be  an 
object  in  the  fundus  of  the  observed  eye.  We  draw  the  ray  be  parallel 


OPHTHALMOSCOPE 


201 


to  the  axis :  it  passes,  after  refraction,  through  the  anterior  focus  of  the 
eye  4>15  and  the  other  rays  coming  from  b  are  parallel  to  it,  since  the  eye 


Fig.  132. 


is  emmetropic.  One  of  these  rays  db'  passes  without  refraction  through 
the  optic  center  of  the  lens,  and  it  is  on  this  ray  db'  that  the  image  b'  of  b 
is  formed,  in  the  focal  plane  of  the  lens.  The  two  triangles  pc^  and 

dfb'  are  similar:  we  have,  therefore,  <.  —  $  >  that  is  to  say,  the  magnifi- 
cation is  equal  to  the  relation  between  the  focal  distance  of  the  lens  and 
the  anterior  focal  distance  of  the  eye.  The  anterior  focal  distance  of  the 
eye  being  15  millimeters  and  that  of  the  lens  77  millimeters,  the  magnifi- 
cation is  -J?-  or  about  5.  We  can  increase  the  magnification  by  using 
a  weaker  lens,  but  the  image  at  the  same  time  moves  away  from  the  lens 
so  that  the  observer  is  obliged  to  move  back,  which  makes  this  way  of 
increasing  the  image  of  little  practical  value.  In  cases  of  persons 
operated  on  for  cataract  it  may  be  useful  to  use  a  stronger  lens  (+  18) 
to  obviate  the  necessity  of  moving  away. 


M  E    II 


Fig.  133.  —  After  Bjcrrum. 


INFLUENCE  OF  REFRACTION  OF  THE  EXAMINED  EYE  ON  THE  MAGNIFI- 
CATION. —  A  glance  at  figure  133  suffices  to  show  that  if  we  place  the 
lens  so  that  its  focus  coincides  with  the  anterior  focus  of  the  eye,  the 


202 


PHYSIOLOGIC  OPTICS 


magnification  is  the  same  whatever  may  be  the  refraction  of  the  exam- 
ined eye  (principle  of  Badal).  (i) 

If  the  lens  is  nearer  the  eye,  as  is  generally  the  case,  the  magnification 
is  greater  in  the  hypermetropic  eye,  less  in  the  myopic  eye  (fig.  134). 
For  this  reason  the  papilla  of  the  astigmatic  eye  is  seen  elongated  in  the 


Fig.  134.  —  After  Bjerrum. 


direction  of  the  meridian  of  least  refraction;  by  moving  the  lens  away 
the  other  meridian  is  elongated  and  finally  that  which  corresponds  to  the 
meridian  of  greatest  refraction  is  seen  to  be  the  greater  just  as  by  the 
erect  image. 

OPHTHALMOSCOPIC  FIELD.  —  In  order  that  the  field  may  be  as  large 
as  possible,  the  lens  must  be  at  a  distance  from  the  eye  almost  equal  to 
its  focal  distance.  Under  these  circumstances  the  image  which  the  lens 
forms  of  the  pupil  of  the  observed  eye  is  very  large  and  fills  the  entire 
lens;  the  iris  disappears  from  the  field. 

We  construct  the  field  as  for  the  erect  image,  by  supposing  the  center 
(P,  fig.  135)  of  the  pupil  of  the  observing  eye  luminous  and  finding 
what  part  of  the  fundus  of  the  eye  it  could  illuminate.  In  drawing 
figure  135,  it  has  been  supposed  that  the  image  Px  of  the  center  of  the 
pupil  of  the  observer  coincides  with  the  nodal  point  K  of  the  observed 
eye,  so  that  the  "rays"  Aa  and  "Bb  suffer  no  refraction :  ab  is  therefore  the 
field,  and  we  note  that  it  does  not  depend  on  the  pupil  of  the  observed 
eye,  since  the  cone  APXB  does  not  touch  its  borders.  The  field  is  limited 
only  by  the  borders  of  the  lens ;  it  is  therefore  preferable  to  use  a  large 
lens  as  they  do  in  England.  If  we  move  the  lens  nearer  or  farther  away, 
so  that  a  larger  part  of  the  cone  AP±B  coincides  with  the  pupil,  it  may 
happen  that  the  latter  may  be  too  small,  so  that  the  iris  intercepts  the 


(1)  This  is  exact  only  if  the  ametropia  is  axial.  In  case  of  &  myopia  (hypermetropia)  of  curvature, 
the  anterior  focus  is  situated  near  the  eye  in  proportion  as  the  refraction  is  greater.  —  Repeating  the 
construction  of  figure  133,  we  see  that  by  making  the  focus  of  the  lens  coincide  with  the  anterior  focus 
of  the  eye  the  magnification  is  greater  in  the  case  of  myopia.  —  The  astigmatic  eye  has  two  anterior 
foci,  one  for  each  principal  meridian ;  to  obtain  the  same  magnification  in  both  meridians,  the  focus  of 
the  lens  must  be  nearer  the  eye  than  the  more  distant  anterior  focus. 


OPHTHALMOSCOPY 


203 


most  peripheral  rays.  The  field  is  then  limited  by  the  iris  of  the  ob- 
served eye,  which  may  be  seen  through  the  lens.  If  the  pupil  is  small, 
it  may  be  difficult  to  hold  the  lens  exactly  at  the  proper  place  for  the  iris 
to  disappear ;  this  is  why  dilatation  of  the  pupil  is  advantageous.  —  It 
must  be  noted,  furthermore,  that  a  small  part  of  the  field  is  well  illumi- 


Patient  ?  Obaenrer 

Fig.  135.  —  Construction  of  the  ophthalmoscopic  field  by  the  inrerted  image. 

nated.  If  we  use  a  concave  mirror  of  20  centimeters  focus,  as  is  cus- 
tomary, we  see  at  the  fundus  of  the  eye  a  quite  distinct  image  of  the 
flame  (because  the  image  formed  by  the  mirror  is  almost  at  the  focus 
of  the  lens  so  that  the  rays  which  meet  the  eye  are  almost  parallel) ;  it  is 
only  the  part  of  the  field  which  corresponds  to  this  image  that  is  illumi- 
nated ;  the  remainder  is  in  darkness.  —  The  illuminated  portion  may  be 
increased  by  using  a  plane  mirror,  but  the  illumination  is  then  less 
bright. 

We  can  see  the  inverted  image  without  any  lens  if  the  patient  is 
myopic  more  than  6  D. ;  by  moving  the  head  from  side  to  side,  we  make 
sure  that  the  vessels  are  displaced  in  the  contrary  direction,  for  we  can 
also  see  the  fundus  of  the  hypermetropic  eye  (by  the  erect  image)  at  a 
sufficiently  great  distance.  The  visual  field  is  very  small  and  the  magnifi- 
cation often  so  great  that  one  vessel  may  fill  half  of  the  field.  The  ex- 
istence of  this  image  is  sufficient  to  establish  the  diagnosis  of  a  strong 
myopia.  —  It  is  often  difficult  to  examine  the  high  degrees  of  myopia 
by  the  erect  image,  and  by  the  inverted  image  the  enlargement  is  some- 
times not  sufficient.  We  can  then  use  this  image  which  the  myopic  eye 
itself  produces,  by  magnifying  it ;  we  make  no  change  from  the  ordinary 
way  of  examining  with  the  inverted  image ;  it  is  only  necessary  to  move 
the  lens  far  enough  away  for  the  image  to  be  formed  between  the  lens 
and  the  observed  eye.  The  lens  then  produces  an  enlarged  virtual  image 
of  this  inverted  image,  which  is  also  inverted  and  situated  farther  be- 


204  PHYSIOLOGIC  OPTICS 

hind ;  to  see  it  distinctly  it  is  often  necessary  to  place  oneself  very  near 
the  lens,  especially  if  one  uses  a  convex  glass  behind  the  mirror.  We 
can  thus  obtain  an  enlargement  nearly  as  great  as  by  the  erect  image 
(Dcmicheri). 

We  can  use  the  examination  by  the  inverted  image  for  the  determina- 
tion of  the  refraction  of  the  eye,  by  measuring  the  distance  from  the 
observed  eye  at  which  the  inverted  image  is  situated,  since  this  distance 
varies  with  the  refraction  of  the  eye.  This  method,  which  was  proposed 
by  Schmidt-Rimplcr,  has  never  become  very  popular. 

The  appearance  of  the  fundus  of  the  eye  is  very  nearly  the  same  with 
both  methods.  Wre  must  except  the  macula,  however,  which,  by  the 
inverted  image,  often  presents  itself  under  a  special  form,  as  an  oval 
spot,  with  the  long  diameter  horizontal,  a  little  larger  than  the  papilla ; 
this  spot  is  dull,  a  little  darker  than  the  rest,  and  surrounded  by  a  bright 
circle,  corresponding  to  the  convexity  of  the  border  of  the  fovea,  which 
acts  as  a  kind  of  convex  mirror.  Analogous  reflexes  often  appear  also 
on  other  parts  of  the  retina,  especially  in  young  subjects.  —  Differences 
of  level  are  observed  by  the  parallactic  displacement  which  is  obtained 
by  subjecting  the  lens  to  a  slight  to-and-fro  movement. 

92.  Ophthalmoscopic  Examination  of  the  Refracting  Media.  —  To  ex- 
amine the  transparency  of  the  refracting  media  it  is  preferable  to  use 
a  weak  illumination ;  we  use  preferably  a  plane  mirror  or  even  a  convex 
mirror.  De  Weckcr  recommended  the  use  of  the  plates  of  Helmholtz 
for  this  examination.  We  see,  indeed,  the  shadows  which  the  opacities 
produce  by  intercepting  a  part  of  the  rays  sent  back  by  the  fundus  of 
the  eye.  If  the  fundus  is  strongly  illuminated,  and  if  the  obstacles  are 
not  completely  opaque,  they  allow  a  part  of  the  light  to  pass  and  the 
shadow  is  less  complete.  —  It  is  useful  to  use  a  strong  magnifying  glass 
for  this  examination  in  order  that  we  may  place  ourselves  very  near  the 
eye.  Otherwise  many  of  the  small  corpuscles  may  escape  in  the  exam- 
ination. 

It  is  quite  rare  for  these  opacities  to  be  visible  by  the  light  which  they 
themselves  reflect.  It  may  happen,  however,  that  we  can  see  the  red 
color  of  hemorrhages  situated  far  forward  in  the  vitreous  body,  or  the 
white  color  of  certain  opacities,  especially  when  using  the  light  in  such 
a  manner  that  it  falls  very  obliquely  along  the  head  of  the  observer. 
In  cases  of  synchisis  scintillans  the  observing  eye  receives  light  regularly 
reflected  by  the  surfaces  of  the  small  crystals  situated  in  the  vitreous 
bodv. 


UPHTHALMOSCOPY 


205 


93.  Skiascopy.  —  This  method  of  examining  ocular  refraction  was 
discovered  by  Cuignet,  who  described  it  under  the  ill-chosen  name  of 
keratoscopy.  It  was  Parent  who  specially  developed  the  method,  and 
it  was  he  who  first  gave  the  correct  explanation  of  it. 

The  observer  takes  his  place  at  one  meter  from  the  patient,  whose 
eye  he  illuminates  with  a  plane  mirror ;  by  rotating  the  mirror  around  a 
vertical  axis  we  see  the  luminous  spot  on  the  face  of  the  patient  move 
in  the  same  direction.  The  illumination  of  the  pupil  follows  the  same 
direction,  whether  the  patient  be  hypermetropic,  emmetropic  or  very 
slightly  myopic.  —  If  the  myopia  is  over  I  D.,  the  pupillary  light  is  dis- 
placed in  the  contrary  direction,  and  if  the  myopia  is  equal  to  I  D.,  we 
do  not  see  the  light  move  in  the  pupil.  The  luminosity  diminishes 
uniformly  in  the  entire  extent  of  the  pupil  to  disappear  suddenly. 


Fig.  136.  —  Skiascopy.    Plane  mirror. 

L,  lamp ;  Mlt  first  position  of  the  mirror ;  Ln  image  which  it  forms  of  the  lamp ;  Jlf  retinal 
image.  —  M2,  second  position  of  the  mirror;  L2,  image  of  the  lamp  ;  I2,  retinal  image. 

The  examination  of  figure  136  shows  that  the  retinal  image  moves 
in  the  same  direction  as  the  mirror.  If  the  observed  person  is  hyper- 
metropic, emmetropic  or  myopic  less  than  I  D.,  it  is  the  erect  image 
that  the  observer  sees.  The  light  seems  to  him  to  move  on  the  retina, 
as  it  really  does.  If,  on  the  contrary,  the  myopia  is  greater  than  I  D., 
he  sees  the  light  move  in  the  contrary  direction,  because  the  light  comes 
to  him  from  the  inverted  image  which  he  observes.  —  To  determine  the 
degree  of  ametropia,  we  place  before  the  eye  of  the  patient  stronger 
and  stronger  glasses,  until  the  shadow  covers  the  entire  pupil  at  once ; 
the  patient  has  then  a  myopia  equal  to  i  D. 

If  we  use  a  concave  mirror  we  see,  as  in  the  preceding  case,  the 
luminous  spot  move  on  the  face  of  the  patient  in  the  same  direction  as 


206  PHYSIOLOGIC  OPTICS 

the  mirror.  But  the  retinal  image  of  the  flame  moves  in  a  contrary 
direction:  we  see,  indeed,  on  figure  137,  that  the  image  of  the  flame 
(Lx  L2)  formed  by  the  mirror  goes  in  a  direction  contrary  to  that  of 
figure  136,  whence  it  follows  that  it  is  the  same  for  the  retinal  image. 


t 

Fig.  137.  —  Skiascopy.    Concave  mirror. 

The  letters  have  the  same  signification  as  in  figure  136. 


The  observer  also  sees  the  ocular  glow  move  in  an  opposite  direction 
if  the  observed  person  is  emmetropic,  hypermetropic  or  myopic  less  than 
I  D.  and  in  the  same  direction  if  the  myopia  is  greater  than  I  D. 

Skiascopy  is  important  in  the  search  for  astigmatism  if  we  do  not 
dispose  of  it  with  an  ophthalmometer.  If  the  mirror  be  moved  in  the 
direction  of  one  of  the  principal  meridians,  everything  happens  as  in 
a  non-astigmatic  eye.  But  if  the  movements  of  the  mirror  take  place 
in  another  meridian,  the  shadow  is  seen  to  move  in  a  direction  which 
forms  an  angle  with  that  of  the  mirror.  This  is  due  to  the  elliptical 
form  of  the  diffusion  spot.  If  we  draw  an  ellipse  with  oblique  axes  on 
a  sheet  of  paper,  and  observe  it  through  a  smaller  circular  aperture, 
while  giving  it  a  horizontal  movement,  it  is  almost  impossible  not  to 
give  way  to  the  illusion  that  the  motion  takes  place  in  an  oblique  direc- 
tion. —  We  then  find  the  motion  to  give  the  mirror  in  order  that  the 
displacement  of  the  ocular  glow  takes  place  parallel  to  that  of  the  mirror. 
We  then  determine  the  refraction  of  the  principal  meridians  in  the 
ordinary  way. 

When  the  ametropia  is  considerable,  the  glow  is  quite  feeble  and  the 
boundary  between  the  light  and  shade  is  curved.  If  on  the  contrary  the 
eye  is  almost  corrected,  we  see  the  glow  very  bright  and  its  border  is 
very  nearly  straight. 


OPHTHALMOSCOPT 


207 


The  explanation  of  this  fact,  which  has  given  rise  to  a  lively  discus- 
sion, is  quite  simple.  As  the  lamp  (or  its  image  formed  by  the  mirror) 
is  far  from  the  observed  eye,  there  is  formed  in  the  emmetropic  eye  a 
small  pretty  distinct  retinal  image  of  the  flame  (fig.  138,  A).  As  all  the 
light  is  concentrated  on  this  small  image,  it  is  quite  bright  and  although 
it  is  small,  it  nevertheless  fills  the  field  because  the  latter  is  also  very 
small,  as  it  is  easy  to  see  by  using  the  construction  we  have  given  for 


O 


Fig.  138.  —  The  thick  circle  indicates  the  limits  of  the  skiascopic  field :  A,  in  an  emme- 
tropic eye ;  B,  in  a  strongly  ametropic  eye.  The  square  in  A  represents  the  image  of 
the  flame ;  in  B,  it  changes  into  a  large  spot  composed  of  circles  of  diffusion. 

the  ophthalmoscopic  field.  The  right  border  of  the  ocular  glow  cor- 
responds with  the  border  of  the  retinal  image  of  the  flame.  In  the 
ametropic  eye  the  field  is  large,  and  the  retinal  image  is  displaced  by  a 
diffusion  spot,  much  larger  and  consequently  not  so  bright.  Each  point 
of  the  distinct  retinal  image  is  replaced  by  a  circle  of  diffusion  of  the 
same  form  as  the  pupil  of  the  observed  eye;  as  the  latter  is  generally 
round,  the  spot  also  takes  on  a  round  form  (fig.  138,  B)  more  pro- 
nounced in  proportion  as  the  ametropia  is  greater.  It  is  easy  to  prove 
the  exactness  of  this  explanation:  if  we  use  as  luminous  source  a  very 
long,  bright  line,  the  border  of  the  ocular  glow  remains  straight,  even 
in  the  case  of  strong  ametropia,  because  the  superposition  of  the  circles 
of  diffusion  cannot  then  produce  a  round  form.  Likewise,  if  we  give 
the  pupil  a  triangular  form,  by  placing  a  stenopaic  opening  of  this  form 
before  the  eye  of  the  observed  person,  the  shadow  retains  also  its 
rectilinear  border,  for  the  supposition  of  triangular  diffusion  spots  can- 
not give  a  round  form  to  the  diffusion  spot. 

But  in  neither  case  does  the  observer  see  a  distinct  image,  because 
his  eye  is  accommodated  for  the  pupillary  plane  of  the  observed  eye, 


2Q8 


PHYSIOLOGIC  OPTICS 


while  the  image  which  he  observes  is  in  front  of  (M)  or  behind  (H)  this 
plane.  And  as  it  is  not  focused  for  the  image,  the  latter  is  seen  vaguely, 
each  point  being  represented  by  a  circle  of  diffusion,  the  border  of  which, 
as  always,  corresponds  with  the  border  of  the  pupil  of  the  observer. 

THEORY  OF  LEROY.  —  The  explanation  which  Leroy  has  given  of 
skiascopy,  and  which  is  widely  accepted,  especially  in  Germany  is  in 


Patient 


Observer 


Fig.  139. 


thorough  agreement  with  that  of  Parent  which  I  have  just  explained. 
Let  a  (fig.  139)  be  an  illuminated  point  of  the  retina  of  the  observed  eye, 
supposed  to  be  myopic,  and  a'  its  image.'  From  the  observed  eye  then 
starts  the  luminous  cone  ba'c,  of  which  the  part  a'mo  enters  the  observ- 
ing eye.  This  eye  sees  luminous  the  part  of  the  pupil  which  sends  rays 
to  it,  that  is  the  part  bp,  while  pc  is  dark  because  the  rays  which  conic 


Fig.  140.  B 

from  this  part  are  intercepted  by  the  iris  of  the  observer.  This  Leroy 
somewhat  subtly  expressed  by  saying  that  the  shadow  is  produced  by 
the  iris  of  the  observer.  We  can  imagine  the  pupil  of  the  observer 
projected  through  a'  on  the  pupil  of  the  observed  person  (fig.  140,  A) ; 
the  part  of  this  latter  which  it  would  cover  would  appear  luminous.  In 
regard  to  the  theory  of  Parent,  we  would  say  that  the  observer  sees  the 
point  a  but  dimly,  that  is  to  say  as  a  diffusion  circle  the  border  of  which, 


OPHTHALMOSCOPY 


209 


as  we  know,  corresponds  to  the  border  of  the  pupil  of  the  observed 
eye. 

The  two  theories  are  therefore  two  different  ways  of  saying  the  same 
thing.  But  were  the  curved  form  of  the  shadow  explained  by  the  form 
of  the  pupil  of  the  observer  it  would  be  wrong,  because  the  phenomena 
do  not  change  if  the  observer  looks  through  a  triangular  aperture  placed 
in  front  of  his  pupil.  The  form  of  the  pupil  of  the  observer  plays  no 
part,  for  in  reality  it  is  not  a  luminous  point  which  is  found  on  the  retina, 
as  the  theory  of  Leroy  supposes,  but  an  image  of  the  flame  of  which 
ad  (fig.  139)  is  a  section.  The  border  of  the  image  which  \ve  use  is, 
therefore,  a  straight  line  perpendicular  to  the  plane  of  the  paper,  and 
it  would  be  necessary  to  repeat  the  construction  of  Leroy  for  each 
point  of  this  straight  line.  We  would  thus  obtain  a  series  of  projections 
of  the  pupil  of  the  observer,  which  would  delimit  the  part  of  the  pupil 
of  the  observed  eye  which  appears  luminous  (fig.  140,  B).  It  is  easy  to 
see  that  the  form  of  each  diffusion  circle  has  no  influence  on  the  form 
of  the  border  of  the  shadow. 

PARACENTRAL  SHADOW.  —  When  one  is  near  correction,  one  often 
sees  the  shadow  move  irregularly.  Bitzos  has  described  a  paracentral 
shadow:  a  part  of  the  pupil,  near  the  center,  appears  dark,  while  the 
borders  are  still  illuminated.  This  phenomenon  indicates  that  the  refrac- 


Observer 


Patient 

Fig.  141.  —  Theory  of  the  paracentral  shadow. 

tion  is  not  the  same  everywhere  in  the  pupil;  it  frequently  makes  im- 
possible a  very  exact  determination  of  the  refraction. 

We  must  not,  therefore,  expect  a  very  exact  determination  by  skia- 
scopy,  as  is  the  case  also  for  subjective  measurement  and  determination 
by  the  erect  image,  simply  because  the  very  idea  of  ocular  refraction 
does  not  permit  of  very  great  exactness. 

Here  is  the  explanation  of  the  paracentral  shadow.  Let  us  suppose 
an  eye  emmetropic,  but  with  a  strong  spherical  aberration  so  that  the 


210  PHYSIOLOGIC  OPTICS 

peripheral  parts  of  the  pupil  may  be  myopic.  The  rays  coming  from  a 
luminous  point  of  the  retina  would  then  have  the  direction  indicated  on 
figure  141.  An  eye,  the  pupil  of  which  would  be  at  P  would  receive  rays 
i  and  3  and  would  see  luminous  the  parts  corresponding  with  the  pupil, 
while  at  2  the  pupil  would  appear  dark,  since  the  ray  2  would  not  enter 
the  pupil.  The  observing  eye  would,  therefore,  see  a  bright  center 
separated  from  equally  bright  borders  by  a  dark  ring.  If  P  be  displaced 
a  little  downwards,  it  would  receive  all  the  rays  drawn  on  the  figure, 
but  some  on  the  other  half  would  not  enter  it,  which  would  give  the 
phenomenon  of  paracentral  shadow.  This  shadow  is,  therefore,  nothing 
else  than  the  manifestation  of  spherical  aberration.  We  have  seen  that 
the  appearance  which  indicates  aberration  consists  of  a  luminous  ring 
towards  the  borders  of  the  pupil,  separated  from  the  central  light  by  a 
dark  zone;  tilting  the  mirror  slightly  the  central  light  becomes  partly 
joined  to  the  ring  and  the  dark  part  assumes  the  form  described  by 
Bitzos. 

I  have  several  times  emphasized  the  advantages  which  skiascopy  with 
a  luminous  point  presents  for  the  study  of  optic  anomalies  of  the  eye. 
It  also  lends  itself  very  well  to  the  ordinary  measurement  of  refraction. 
At  the  critical  moment  when  the  movement  of  the  light  changes  its 
direction  the  far  point  of  the  observed  eye  coincides  with  the  pupil  of 
the  observer.  As,  on  the  other  hand,  the  principle  of  Jackson  demands 
that  the  image  of  the  luminous  source  coincide  with  the  far  point  one  is 
led  to  use  a  plane  mirror  and  to  place  the  flame,  surrounded  by  its  opaque 
screen,  quite  near  the  eye  of  the  observer.  But,  in  order  to  observe  the 
luminous  band  of  astigmatism  and  the  ring  of  aberration,  we  must  place 
the  lamp  by  the  side  of  and  a  little  behind  the  patient. 

Bibliography.  —  Cumming  (W.).  Medico-chirurgical  transactions.  XXIX,  p.  284. — 
Briicke  (E.).  J.  Mutters  Archiv  fur  Anatomic  und  Physiologic,  1847,  p.  225.  — Helmholtz 
(H.).  Beschreibung  eines  Augenspiegels  zur  Beobachtung  der  Netzhaut  am  lebenden  Auge.  Ber- 
lin, 1851.  —  Kuete  (Th.).  Der  Augenspiegel  und  das  Optometer.  Gottingen,  1852.  —  Coc- 
cius  (A.).  Ueber  die  Anwendung  des  Augenspiegels,  nebst  Angabe  eines  neuen  Instruments. 
Leipzig,  1853.  —  Cuignet.  Keratoscopie.  Recueil  d'opht.,  1873-74.  —  Parent.  Diagnostic  et 
determination  objective  de  V Astigmatisme.  Kecueil  d'opht.,  1881.  — Leroy  (C.  J.  A.).  Le 
phenomene  de  P  ombre  pupillaire.  Rev.  gen.  d'opht.,  1887,  p.  289.  —  BellarminofF.  Neues 
Verfahren  den  Augenhintergrund  zu  besichdgen.  Munch,  med.  Wochenschrift,  1888.  —  Bit- 
zos  (G.).  La  Skiascopie.  Paris,  1892.  —  Demicheri  (L.).  Examen  ophtalmoscopique  d  Fimage 
renversee  sur  les  yeux  fortement  myopes.  Ann.  d'oc.,  1895. 

The  theory  of  the  ophthalmoscope  is  found  explained  in  several  treatises  on  ophthalmo- 
scopy.  The  following  small  book  is  to  be  recommended  on  account  of  its  brevity  and  clear- 
ness: 

Bjerrum  (I. )  (of  Copenhagen).  Instructions  pour  Temploi  de  I'ophtalmoscope.  Translated 
by  Grosjean.  Paris,  Steinheil,  1894. 


CHAPTER   XIV. 
THE    PUPIL. 


94.  —  To  properly  understand  the  working  of  a  dioptric  instrument, 
we  must  not  only  know  the  position  and  power  of  the  refracting  sur- 
faces, but  also  the  size  and  position  of  its  diaphragm.  I  have  already 
referred  to  the  difference  between  the  size  and  position  of  the  apparent 
pupil  and  the  real  pupil,  and  observed  that  the  pupil  is  generally  dis- 
placed a  little  to  the  temporal  side.  Its  size  varies  in  different  people ; 
generally  it  diminishes  with  age,  and  finally  becomes  quite  small  in  old 
people.  As  a  rule  it  is  larger  in  myopes  than  in  hypermetropes,  at  least 
in  appearance,  for  the  anterior  chamber  of  myopes  is  often  deeper,  which 
makes  the  pupil  appear  larger.  In  cases  of  complete  amaurosis,  the 
pupil  is  immovable  and  very  large,  except  when  the  amaurosis  has  a 
spinal  origin,  in  which  case  the  pupil  is  often  greatly  contracted. 

The  pupil  contracts  and  dilates  under  many  different  influences ;  these 
movements  are  very  complex  and,  for  the  most  part,  still  imperfectly 
elucidated.  All  agree  on  the  existence  of  the  sphincter,  while  that  of  the 
dilatator  is  disputed,  although  physiological  observations  make  its  exist- 
ence probable.  The  movements  of  the  pupil  are  under  the  influence  of  the 
motor  oculi  and  the  great  sympathetic.  Cutting  the  motor  oculi  produces 
a  dilatation  of  the  pupil,  much  less,  however,  than  that  which  may  be  pro- 
duced by  atropine.  The  contractions  which  accompany  accommodation 
and  incidence  of  light  cease  at  the  same  time,  as  well  as  accommodation 
itself.  The  contraction  which  accompanies  incidence  of  light  is,  there- 
fore, produced  by  a  reflex  action  between  the  retina  and  the  optic  nerve 
on  the  one  hand  and  the  oculo-motor  on  the  other.  It  must  be  noted, 
however,  that  Brown-Sequard  produced  a  contraction  of  the  pupil  by 
concentrating  light  on  an  enucleated  rabbit's  eye,  according  to  which 
experiment  the  light  would  also  have  a  direct  influence  on  the  muscles 
of  the  iris.  An  irritation  of  the  oculo-motor  produces  a  contraction  of 
the  pupil,  an  irritation  of  the  great  sympathetic  at  the  neck  produces, 

211 


212  ,  PHYSIOLOGIC   OPTICS 

on  the  contrary,  a  marked  dilatation,  while  the  cutting  of  this  nerve 
contracts  the  pupil. 

95.  Action  of  Mydriatics  and  Myotics.  —  The  instillation  of  a  drop  of 
a  solution  of  atr opine  (0.5  per  cent.)  produces  a  marked  dilatation  of  the 
pupil;  it  paralyzes  its  movements  as  well  as  the  accommodation:  the 
effect  generally  lasts  eight  days.    If  we  use  a  much-diluted  solution,  the 
effect  does  not  last  so  long  and  the  action  on  accommodation  is  much  less 
pronounced.    To  explain  why  the  dilatation  by  atropine  is  much  greater 
than  that  obtained  by  cutting  the  motor  oculi,  it  is  supposed  that  it  acts 
at  the  same  time  by  irritating  the  terminal  fibres  of  the  great  sympa- 
thetic. 

Homatropine  (0.5  per  cent.)  dilates  the  pupil,  but  it  generally  does  not 
act  to  any  extent  on  the  accommodation  if  the  solution  is  pure,  (i)  Its 
effect  lasts  twenty-four  hours. 

Cocaine  (5  per  cent.)  dilates  the  pupil,  but  does  not  act  on  the  accom- 
modation; at  least  I  have  not  been  able  to  find  any  effect  on  my  own 
eye.  (i) 

A  mixture  of  homatropine  and  cocaine  dilates  the  pupil  still  more 
than  either  one  of  these  alkaloids  by  itself.  Such  a  mixture  is  recom- 
mended, therefore,  for  investigations  of  accommodation,  the  more  so 
because  the  pupil  is  dilated  some  time  before  accommodation  begins 
to  diminish.  Scopolamine  (J  per  cent.)  produces  complete  paralysis  of 
accommodation,  with  a  very  marked  dilatation  of  the  pupil  which  we  can 
further  increase  by  adding  cocaine. 

With  a  solution  of  eserine  (0.5  per  cent.)  we  obtain  a  very  great  contrac- 
tion of  the  pupil,  and  the  accommodation  reaches  its  maximum.  I  have 
obtained  with  eserine  a  little  greater  amplitude  than  I  could  produce 
spontaneously.  It  is  doubtful  whether  eserine  acts  directly  on  the 
sphincter,  or  whether  the  contraction  of  the  pupil  is  analogous  to  that 
which  always  accompanies  accommodation. 

96.  The  Movements  of  the  Pupil. 

i°  The  pupil  contracts  under  the  influence  of  light  (reflex  by  the  optic 
nerve).  It  is  not  alone  the  light  which  strikes  the  retina  of  a  particular 
eye,  but  also  that  which  enters  the  other  eye,  which  causes  the  contrac- 
tion. The  pupils  are  equal  in  size,  even  if  one  eye  is  exposed  to  a  much 
stronger  light  than  the  other.  If  the  pupil  does  not  contract  when  the 
light  strikes  the  retina  of  the  same  eye,  and  does  contract  when  it  strikes 

(I)  Other  observers  maintain  the  contrary;  the  differences  are  perhaps  individual ;  perhaps  due  to 
the  fact  that  they  use  different  preparations. 


THE  PUPIL  213 

that  of  the  other  eye,  we  may  infer  a  complete  amaurosis  of  the  eye  in 
question.  In  complete  darkness  the  pupil  reaches  its  maximum  dilata- 
tion, so  that  the  iris  is  often  not  visible  (i)  (Colin,  CL  Dubois-Reymond). 
This  fact  has  been  demonstrated  by  taking  photographs  of  the  eyes  in 
complete  darkness:  we  illuminate  them  with  mixtures  of  powders,  the 
light  of  which  does  not  continue  long  enough  to  give  the  pupil  time  to 
contract.  It  is  not  easy  to  reconcile  this  observation  with  every-day 
experience,  which  shows  that  the  reaction  of  the  pupil  to  light  depends 
on  the  oculo-motor,  the  cutting  of  which  produces  only  a  medium  dila- 
tation. 

It  is  manifest  that  the  object  of  this  contraction  of  the  pupil  is  to 
regulate  the  quantity  of  light  that  enters  the  eye. 

2°  The  pupil  contracts  during  accommodation.  —  To  examine  the  func- 
tions of  the  pupil  we  must  see  whether  it  contracts :  a)  when  the  light 
strikes  the  retina  of  the  same  eye ;  b)  when  the  light  strikes  the  retina  of 
the  other  eye;  c)  when  the  patient  makes  an  effort  of  accommodation. 
We  know  that  accommodative  contraction  may  exist  without  the  reac- 
tion to  light,  and  vice  versa  (Argyll  Robertson).  The  accommodative  con- 
traction has  this  peculiarity  that  even  the  most  peripheral  parts  of  the 
iris  show  a  centripetal  movement,  which  is  not  generally  the  case  for 
the  reaction  to  light  (Hueck). 

The  object  of  this  contraction  is  to  eliminate  the  action  of  the  periph- 
eral parts  of  the  crystalline  lens,  which  do  not  sufficiently  accommodate. 

3°  The  pupil  contracts  when  the  aqueous  humor  escapes.  —  I  have  already 
remarked  that  this  contraction  is  also  observed  after  death  (Arlt),  so 
that  it  must  be  considered  as  a  purely  mechanical  phenomenon,  which 
we  may  identify  with  accommodative  contraction.  I  have  made  some 
experiments  to  elucidate  the  nature  of  this  contraction ;  before  describ- 
ing them  it  is  important  to  speak  of  the  posterior  chamber,  the  existence 
of  which  has  been  disputed. 

On  examining  an  eye  by  oblique  illumination,  we  easily  see  that  the 
border  of  the  iris  is  in  contact  with  the  crystalline  lens.  We  also  see 
this  very  well  by  examination  with  the  third  image  of  Purkinje,  which  I 
have  mentioned  page  42,  or  by  examining  an  eye  affected  with  mature 
cataract.  If  we  remove  the  crystalline  lens  from  the  eye,  or  if  it  be  dis- 
located, the  iris  shows  at  each  movement  of  the  eye  the  trembling  known 
as  iridodonesis;  Helmholtz  and  others  were  led  to  infer  from  these  facts 
the  non-existence  of  a  posterior  chamber ;  there  exists,  nevertheless,  a 

(1)  If  the  iris  is  not  visible  at  all,  it  is  an  apparent  phenomenon,  due  to  refraction  through  the  cor- 
nea, for  if  we  plunge  an  eye,  the  pupil  of  which  is  dilated  to  this  extent,  in  water,  the  iris  becomes  im- 
mediately visible  (Stadfcldt). 


214  PHYSIOLOGIC  OPTICS 

small  space  filled  with  liquid  between  the  crystalline  lens,  the  ciliary 
body  and  the  peripheral  parts  of  the  iris.  We  sometimes  see  in  perfect 
eyes  a  slight  trembling  of  the  peripheral  parts  of  the  iris  when  the  eye 
makes  a  movement. 

The  observation  of  Arlt,  showing  that  we  still  see  the  pupillary  con- 
traction after  paracentesis  has  been  performed  on  the  dead  eye,  struck 
me  forcibly.  To  verify  it  I  introduced  the  point  of  a  Pravaz  syringe  into 
the  anterior  chamber ;  by  depressing  or  withdrawing  the  piston  we  can 
make  the  pupil  contract  or  dilate  at  will.  By  removing  nearly  all  the 
contents  of  the  anterior  chamber  I  was  able  to  reduce  the  diameter  of 
the  pupil  to  i  or  2  mm.  On  the  contrary,  by  forcing  the  injection  as  far 
as  possible,  the  dilatation  may  extend  so  far  as  to  make  the  iris  disap- 
pear, (i)  It  is  true  that  one  part  of  the  change  is  only  apparent,  as 
Stadfeldt  has  shown:  the  more  the  pupil  recedes,  the  more  enlarged 
it  is  seen  through  the  cornea;  but  on  examining  the  eye  under  water, 
we  find  a  very  noticeable  change.  The  phenomenon  is  difficult  to  ex- 
plain ;  it  is  not  due  to  the  mere  effect  of  pressure,  for  we  may  compress 
the  eye  all  we  want  to  without  observing  any  change  in  the  diameter  of 
the  pupil ;  nor  is  it  due  to  a  difference  of  pressure  between  the  chamber 
and  the  posterior  part  of  the  globe,  for,  by  injecting  liquid  into  the 
vitreous  body  or  by  removing  it,  we  no  longer  produce  any  change  of 
the  pupil. 

I  also  injected  a  solution  of  gelatine  into  the  anterior  chamber,  and 
then,  by  hardening  the  eyes  slightly,  I  obtained  pretty  fair  casts.  Under 
these  circumstances  the  posterior  chamber  is  also  always  injected;  the 
cast  forms  a  prismatic  ring,  with  an  anterior  surface  corresponding  to 
the  iris,  a  posterior  surface  corresponding  to  the  anterior  surface  of  the 
crystalline  lens  and  an  external  surface  corresponding  to  the  ciliary 
body.  But,  between  the  crystalline  lens  and  the  part  of  the  iris  next  to 
the  pupil,  we  never  find  any  gelatine,  or  if  there  is  any,  it  is  so  thin  a 
layer  that  it  is  destroyed  in  the  work  of  preparation. 

4°  During  sleep  the  pupil  is  greatly  contracted,  even  in  amaurotic 
persons,  whose  pupil  generally  is  large  and  motionless.  The  pupil  is  also 
contracted  during  narcosis,  and  generally  when  a  person  is  in  agony :  at 
the  moment  of  death  it  is  generally  greatly  dilated;  this  dilatation  dis- 
appears immediately.  In  spite  of  the  pupillary  contraction  during  sleep 
the  reaction  to  light  persists. 

5°  On  examining  the  pupil  with  a  magnifying  glass  we  observe 
rhythmic  contractions,  which,  at  least  in  part,  correspond  to  the  systole, 

(1)  When  we  increase  the  pressure  much,  the  cornea  becomes  opaque;  we  can  make  it  almost  as 
white  as  the  sclera ;  as  soon  as  the  pressure  ceases,  it  again  becomes  transparent. 


THE  PUPIL 


215 


and  which  are  due  to  the  fact  that  the  vessels  are  filling  with  blood.  The 
contraction  is  greater  when  the  systole  coincides  with  an  expiration. 
We  cannot  explain  in  this  way  all  the  slight  contractions  of  the  pupil 
which  are  observed  with  a  magnifying  glass. 

6°  We  observe  a  dilatation  of  the  pupil  following  fright ;  it  also  accom- 
panies dyspnea,  vigorous  muscular  action  or  a  sharp  irritation  of  any 
sensitive  nerve. 

97.  Advantage  of  the  Position  of  the  Pupil  near  the  Nodal  Point.  — 

Young  remarked  that  if  the  pupil  had  been  situated  farther  forward  in 
the  eye  the  apparent  size  of  objects  would  have  changed  every  time  we 
made  an  effort  of  accommodation.  We  have  seen  that  the  image  of 
a  point  for  which  the  eye  is  not  accommodated,  forms  a  circle  of  diffu- 


Fig.  142. 

sion,  the  center  of  which,  corresponding  to  the  middle  of  the  pupil,  is 
frequently  brighter  on  account  of  spherical  aberration ;  if  the  pupil  is  not 
too  large  we  may  consider  this  center  as  a  vague  image  of  the  point. 
Suppose  that,  in  a  state  of  repose,  the  eye  is  focused  for  the  object  AB 
(fig.  142).  The  image  of  the  point  A  is  formed  at  Al  on  the  line  AM 
passing  through  the  nodal  point.  During  accommodation  the  image  is 
moved  forward  to  A2.  To  find  the  place  where  the  diffuse  image  is 
formed  on  the  retina  we  draw  the  ray  Ap  passing  through  the  middle  of 
the  pupil  of  entrance :  after  refraction,  this  ray  must  pass  through  pv  (i), 
the  middle  of  the  pupil  of  exit,  and  through  A2;  the  diffuse  image  is 

(1)  On  the  fiarure  we  suppose  that  p  and  pi  coincide ;  really  they  are  about  0.7  millimeters  apart. 


216  PHYSIOLOGIC   OPTICS 

therefore  formed  at  A3  and  the  image  of  the  entire  object  A3  B3  is 
smaller  than  the  distinct  image  Ax  B±.  In  the  human  eye  we  may  ob- 
serve a  slight  effect  of  this  kind  by  using  our  accommodation  while 
observing  distant  objects;  it  is  more  pronounced  when  we  replace  the 
pupil  by  a  stenopaic  opening,  at  some  distance  from  the  eye. 

The  position  of  the  pupil  near  the  nodal  point  has  probably  still  an- 
other advantage.  One  of  the  first  qualities  that  we  require  in  a  photo- 
graphic objective  is  that  it  be  rectilinear,  that  is  to  say,  that  the  images 
of  the  straight  lines  placed  peripherally  in  the  field  be  straight,  and  not 
curved.  We  usually  obtain  this  effect  by  placing  the  diaphragm  in  the 
nodal  plane,  and  the  position  of  the  pupil  near  the  nodal  point  of  the 
eye  seems  to  play  a  part  for  the  correct  vision  of  objects  seen  indirectly. 
Nevertheless,  the  eye  is  not  rectilinear.  It  follows  from  a  series  of 
experiments  described  by  Helmholtz  that,  in  indirect  vision,  the  straight 
lines  appear  in  the  form  of  curves,  the  concavity  of  which  is  turned 
towards  the  point  fixed.  If  we  desire  to  repeat  these  experiments,  we 
must  place  ourselves  so  that  no  other  line,  which  we  know  to  be  straight, 
is  in  the  field,  for  example  by  stooping  over  a  large  table. 

i°  We  place  on  the  table  a  small  piece  of  paper  A  (fig.  143),  which 

serves  as  a  point  of  fixation,  and  two  others,  B  and  C,  as  far  as  possible 

from  A,  without  ceasing  to  see  them  distinctly  in 

•B      indirect  vision.    While  fixing  A,  we  try  to  place 

a  fourth  piece,  D,  on  the  straight  line  which  joins 

B  and  C.    We  shall  nearly  always  place  it  too  far 

inwards. 

2°  If  we  place  on  the  table  a  strip  of  paper  with 
parallel  borders,  8  to  10  centimeters  in  width,  and 
fix  the  center  of  it,  the  borders  appear  concave 
towards  the  point  of  fixation.  The  strip,  there- 
fore, appears  larger  at  the  middle  than  towards 
the  ends. 

3°  Guided  by  theoretical  considerations,  the 
value  of  which  may  appear  doubtful,  Helmlioltz 
designed  the  hyperbolic  chess-board,  of  which 

figure  144  is  an  illustration  diminished  in  the  proportion  of  3/16.  In 
accordance  with  his  theory,  he  found  that,  placed  at  a  distance  of  20 
centimeters,  for  which  the  chess-board  was  calculated,  he  saw  the  curves 
assume  the  appearance  of  straight  lines  when  he  fixed  the  middle.  When 
he  stood  at  a  greater  distance,  the  lines  appeared  to  have  the  curvature 
which  they  really  had ;  moving  nearer  and  nearer,  he  saw  the  curvature 


THE  PUPIL  217 

diminish  and  finally  completely  disappear.  The  distance  at  which  the 
curvature  disappeared  was  each  time  almost  exactly  20  centimeters.  If 
he  approached  nearer  still,  the  lines  presented  the  reverse  curvature, 
appearing  concave  towards  the  middle. 


Fig.  144.  —  Hyperbolic  chess-board  of  Helmhoitz. 

4°  Another  experiment  of  the  same  kind  consists  in  placing-  a  circular 
piece  of  cardboard  in  the  periphery  of  the  visual  field;  above  or  below 
we  see  it  elongated  in  the  horizontal  direction,  while  on  the  two  sides  it 
appears  elongated  in  the  vertical  direction. 

We  can  express  all  these  phenomena  by  saying  that  the  visual  field  is 
seen  narrowed  towards  the  periphery.  Let  us  suppose  the  plane  visual 
field  divided  into  equidistant  zones,  and  suppose  that  we  gave  an  illus- 
tration of  it  by  making  the  zones  diminish  towards  the  periphery.  We 
would  thus  obtain  analogous  deformities ;  the  straight  lines  would  be 
represented  by  curves  concave  towards  the  middle  (see  page  98).  A 
circle  placed  peripherally  in  the  field  would  become  narrower  in  the 
radial  direction,  and  so  forth. 

To  explain  these  observations,  Hclmholts  called  attention  to  another 
observation  which  he  made,  and  which  is  itself  a  consequence  of  the  law 
of  Listing  (see  chapter  XIX). 

Standing  in  front  of  a  wall  we  look  at  a  point  A  situated  on  a  level 
with  the  eyes;  we  then  raise  the  look,  without  changing  the  position 
of  the  head,  towards  the  horizontal  line  which  forms  the  upper  edge  of 
the  wall.  Moving  the  look  rapidly  along  this  line,  we  see  it  concave, 
with  the  concavity  turned  downwards  exactly  as  we  would  see  it  in  indi- 
rect vision  by  fixing  the  point  A,  if  it  was  sufficiently  distinct. 

Faithful  to  the  empiric  theories  by  which  he  tried  to  explain  most 


218  PHYSIOLOGIC  OPTICS 

observations  on  physiologic  optics,  Helmholtz  supposed  that  this  illu- 
sion was  the  cause  of  the  preceding  one.  Surveying  the  line  with  the 
look  it  appears  curved  on  account  of  the  law  of  Listing,  and  it  is  because 
we  have  thus  learned  that  it  appears  curved  that  it  does  usually  appear 
so  in  indirect  vision  also.  —  We  must  note  that  this  way  of  observing 
the  line,  namely  by  surveying  it  with  the  raised  look,  appears  altogether 
unusual.  I  do  not  think  that  before  making  this  experiment  I  ever 
looked  at  a  line  in  this  way,  as  it  would  be  more 
natural  for  me  to  raise  my  head  to  look  at  it,  and  in 
this  case  the  illusion  disappears.  It  is,  therefore,  not 
easy  to  understand  how  I  would  have  known  that  the 
line  ought  to  appear  curved. 

But  the  following  experiment  is  still  more  at  vari- 
ance with  the  explanation  in  question.  I  had  con- 
structed a  small  artificial  eye  (fig.  145),  all  the  dimen- 
sions of  which  approached  as  nearly  as  possible  those 
of  the  human  eye.  The  cornea  and  the  crystalline  lens 
are  of  glass,  and  have  the  same  curvature  as  in  the 
human  eye;  in  order  to  remedy  somewhat  the  exces- 
sive refraction  of  the  crystalline  lens,  I  filled  the  eye 
Fig"l45.  with  a  mixture  of  glycerine  and  water,  the  index  of 

Artificial  eye.  which  is  a  little  higher  than  that  of  the  vitreous  body. 
The  retina  is  replaced  by  a  hollow  hemisphere  of  ground  glass,  having 
nearly  the  curvature  of  the  retina  of  the  human  eye.  Although  the 
refraction  may  not  be  absolutely  identical  with  that  of  the  human  eye, 
the  difference,  however,  cannot  be  very  great. 

With  this  eye  I  repeated  and  succeeded  in  all  the  experiments  cited 
above  (fig.  146).  The  image  of  the  black  strip  has 
the  borders  convex  towards  the  periphery;  in  order 
that  the  borders  of  the  image  appear  straight  those 
of  the  object  must  be  concave.  The  image  of  a  circle 
appeared  shrunken  in  the  radial  direction,  etc.  The 
experiment  with  the  chess-board  of  Helmholtz  is  still 
more  conclusive.  As  long  as  the  eye  is  at  a  great 
distance,  the  image  is  like  the  object;  but,  according  Jf*  window 
as  we  move  the  eye  nearer,  the  curvature  of  the  lines  artificial  eye. 
becomes  obliterated,  and  very  close  to  the  drawing  the  lines  of  the 
image  appear  concave  on  the  inside.  I  tried  to  determine  the  place 
where  the  direction  of  the  curvature  changes,  or  in  other  words  the 
place  where  the  figure  appears  most  rectilinear,  and  each  time  I  found 


THE  PUPIL  219 

a  distance  of  20  centimeters,  at  least  as  exactly  as  when  making  the 
experiment  with  my  own  eye. 

According  to  this  experiment  it  seems  to  me  beyond  doubt  that  all 
these  deformities  depend  primarily  upon  the  form  of  the  retina.  Pro- 
jecting a  plane  on  a  hollow  sphere,  we  necessarily  obtain  towards  the 
periphery  a  narrowing  of  the  projection  analogous  to  that  which  we 
have  found  for  the  eye.  It  is  possible,  however,  that  the  position  of  the 
pupil  in  front  of  the  nodal  point  may  play  a  certain  part,  for  the  illusion 
appears  to  me  rather  more  pronounced  if  I  look  through  a  stenopaic 
opening,  which  acts  as  an  artificial  pupil  placed  in  front  of  the  eye. 

This  touches  one  of  the  fundamental  questions  of  physiologic  optics. 
I  wish  to  speak  of  the  antagonism  between  the  nativistic  and  the  empiric 
ideas.  Although  this  question  is  beyond  the  scope  of  the  present  work, 
I  shall  consider  it  for  a  moment. 

Looking  at  a  window,  the  visual  sense  tells  me  that  it  is  square.  How 
can  the  eye  give  this  information  ?  The  nativists,  among  whom  we  must 
first  mention  Hering,  say  that,  by  an  unknown  congenital  mechanism, 
the  retinal  impression  gives  directly  to  the  mind  the  idea  of  the  form 
of  the  object.  We  could  express  this  idea  by  saying  that,  by  an  un- 
known mechanism,  the  mind  sees  the  retinal  image.  The  empiricists, 
among  whom  Helmholtz  is  the  most  celebrated,  say  that  the  retinal  image 
gives  us  primarily  no  information  on  the  form  of  the  object,  that  it  is 
only  a  "sign"  of  the  object,  almost  as  the  letter  A  is  the  sign  of  a  certain 
sound ;  by  the  movements  of  the  eyes  and  by  information  furnished  by 
the  touch,  we  learn  that  this  sign  is  to  tell  us  that  the  object  is  square ; 
Helmholtz  expressed  his  ideas  thus :  "As  for  me,  I  think  it  probable  that 
the  figure,  form  and  position  of  the  true  retina,  as  well  as  the  deformities 
of  the  retinal  image,  are  absolutely  unconcerned  with  vision,  provided 
the  image  be  distinct  in  its  whole  length,  and  that  the  form  of  the  retina 
and  that  of  the  image  remain  perceptibly  invariable  from  one  moment 
to  another.  We  have  absolutely  no  knowledge  of  the  existence  of  our 
retina." 

Under  the  influence  of  Darwin,  an  effort  was  made  (Bonders)  to  recon- 
cile the  two  schools  by  saying  that  the  qualities  in  question  are  the 
result  of  experiences,  not  of  the  individual,  but  of  the  species.  Under- 
stood in  this  sense  the  empiric  ideas  scarcely  differ  from  the  nativistic 
ideas,  the  qualities  being  then  congenital  in  the  same  sense  as,  for 
example,  the  actual  form  of  our  organs,  and  we  would  then  have  to 
distinguish  sharply  between  what  we  may  suppose  learned  by  the  same 
individual  and  what  is  due  to  the  experience  of  the  species. 


220  PHYSIOLOGIC   OPTICS 

The  empiric  theories  are  more  attractive  because  they  make  an 
attempt  at  explanation,  while  the  nativistic  theories  exclude  all  hope. 
But  it  would  be  necessary  to  apply  them  only  to  the  phenomena  for 
which  they  readily  adapt  themselves,  and  it  seems  to  me  that  the  great 
physicist  of  Berlin  has  gone  too  far  in  being  willing  to  deny  the  relation 
between  the  illusions  here  described  and  the  deformities  of  the  retinal 
image.  It  seems  to  me  that  there  must  exist  a  mechanism  by  which  we 
can  account  for  the  existence  of  these  deformities. 

Bibliography.  —  The  opposition  to  the  too  free  application  of  empiric  ideas  does  not 
date  from  yesterday.  See  (Euvres  de  Young,  p.  239.  "  We  are  certainly  obliged  every  mo- 
ment to  call  experience  to  our  aid  in  order  to  correct  the  errors  of  one  of  the  senses  by  com- 
parison with  the  perceptions  of  the  others.  [But]  it  seems  to  me  that  some  scientists  go 
too  far  when  they  assert  that  the  use  of  all  our  senses  is  derived  from  experience  alone  with- 
out being  willing  to  admit  the  existence  of  an  instinct  on  a  par  with  it,"  etc. 

Arlt  (F.).  Zur  Anatomic  des  Auges.  Arch.  f.  Ophth.  Ill,  2.  —  Du  Bois-Reymond  (G.). 
Ueber  Photographieen  der  Augen  bei  Magnesiumblitz.  Arch.  f.  Physiologic,  1888,  p.  394.  — 
Tscherning  (M.).  La  contraction  de  I'iris  accompagnant  I'ecoulement  de  Fhumeur  aqueuse.  Bull, 
de  la  Soc.  fran9.  d'opht.,  1885,  p.  305.  —  Tscherning  (M.).  Quelques  consequences  de  la  loi  de 
Listing.  Ann.  d'oc.,  Sept.,  1888.  —  Tscherning  (M.).  La  deformation  des  objels  rus  indireetf- 
ment.  Bull,  de  le  Soc.  franc,  d'opht.,  1895,  p.  403. 


BOOK  II 

FUNCTIONS  OF  THE  RETINA 


CHAPTER   XV. 

CHANGES  WHICH  THE  RETINA  UNDERGOES 

UNDER  THE  INFLUENCE  OF  LIGHT 

98.  --  The  sensitive  layer  of  the  retina  is,  in  all  probability,  that  with 
the  cones  and  rods.  Besides  the  fact  that  the  very  structure  of  the  layer 
makes  this  hypothesis  probable,  it  is  further  strengthened  by  the  experi- 
ments and  measurements  of  H.  Midler  (on  the  entoptic  vision  of  the 
vessels,  see  page  155)  as  well  as  by  observations  on  visual  acuity.  But 
we  have  not  succeeded  in  explaining  in  a  satisfactory  manner  the  mech- 
anism by  which  light  is  transformed  into  nervous  action.  We  have  suc- 
ceeded in  proving  a  certain  number  of  changes  which  the  retina  under- 
goes under  the  influence  of  light,  and  we  have  studied  on  the  other  hand 
the  functions  of  the  retina,  which  are  now  very  well  known,  but  we  have 
not  succeeded  in  explaining  their  mutual  relations. 

RETINAL  PURPLE.  —  If  we  examine  the  eye  of  an  animal  which  has 
been  left  in  darkness  for  some  time  before  enucleation,  we  find  that  the 
external  segment  of  the  rods  has  a  purple  color  which  disappears  very 
quickly  under  the  influence  of  daylight,  passing  through  a  yellow  tint. 
The  cones  have  not  this  coloration  and  the  fovea  of  the  human  eye,  which 
is  composed  of  cones  only,  is  without  color.  If  we  expose  the  eye  of  a 
living  rabbit  to  daylight  for  a  quarter  of  an  hour,  the  purple  first  changes 
to  a  yellow  and  then  completely  fades  away.  Placing  it  so  that  the  image 
of  a  bright  object,  a  window  for  example,  may  be  formed  on  the  retina, 
we  can  thus  obtain  a  permanent  image  (optogram).  If,  after  having 
caused  the  purple  to  fade  away,  we  leave  the  animal  in  darkness,  the 
purple  color  returns  gradually,  provided  that  the  retina  be  in  contact 

221 


222  PHYSIOLOGIC   OPTICS 

with  the  pigment  cells.  It  is  not  necessary  that  they  be  the  pigment 
cells  of  the  same  animal :  if  we  place  the  retina  of  one  eye  in  the  place 
of  that  of  another  eye  the  reproduction  of  the  purple  is  also  effected  in 
darkness. 

Vision  does  not  depend  on  the  retinal  purple,  since  there  is  no  purple 
in  the  fovea,  since  rabbits  whose  retinae  we  have  allowed  to  fade  away 
completely  are  not  blind,  and  since  there  are  certain  classes  of  animals, 
serpents  for  example,  in  which  the  purple  is  wanting. 

The  retinal  purple  was  discovered  by  Boll  in  1876 ;  subsequently  Kuehne 
labored  much  with  the  question,  studying  especially  the  chemical  proper- 
ties of  the  retinal  purple  and  yellow.  The  enthusiasm  with  which  the 
discovery  of  Boll  was  first  received  quickly  grew  cold  when  it  was  seen 
that  it  did  not  give  a  direct  explanation  of  the  mechanism  of  vision. 
Some  time  ago  the  question  was  again  taken  up  and  an  effort  made  to 
put  the  retinal  purple  in  relation,  on  the  one  hand,  with  the  vision  of 
certain  colors,  on  the  other  with  the  adaptation  of  the  retina  to  very 
feeble  light.  These  efforts,  some  of  which  will  be  mentioned  later  on, 
have,  up  to  the  present,  only  a  hypothetic  character. 

99.  Movements  of  the  Pigment  under  the  Influence  of  Light.  —  By  ex- 
perimenting with  frogs,  Boll  observed  yet  another  phenomenon  depend- 
ent on  the  influence  of  light.  He  observed  that  it  was  easy  to  separate 
the  retina  from  the  epithelium  when  the  animals  are  left  in  darkness  for 
an  hour  or  two  before  death.  If  the  animal  has  been  exposed  to  light 
for  a  certain  period  before  enucleation  it  is,  on  the  contrary,  difficult 
to  separate  them,  and  if  we  sever  the  retina  we  find  it  covered  with 
black  pigment  spots  which  adhere  to  it.  We  know  that  the  epithelial 
cells  send  prolongations  between  the  rods  which  they  separate  from  one 
another.  In  darkness  the  pigment  is  found  massed  between  the  exterior 
segments  of  the  rods,  but  under  the  influence  of  light  it  is  displaced  so 
as  to  cover  the  terminal  surface  of  the  rod,  and  is  projected  among  the 
rods,  sometimes  even  to  the  external  limiting  membrane.  The  external 
segment  of  the  rod  is  swollen  at  the  same  time.  Analogous  phenomena 
have  been  described  in  the  eyes  of  birds,  mammals,  and  also  in  a  human 
eye. 

Van  Gendercn  Stort  made  a  step  in  advance  in  the  biology  of  the  retina 
by  using  a  method  by  which  the  retina  is  hardened  in  a  very  little  while 
(nitric  acid) ;  instead  of  cutting  the  retina  with  a  microtome  he  hacked 
it  with  a  razor.  He  showed  that  there  is  yet  another  change  which  the 
retina  undergoes  when  exposed  to  light.  In  an  animal  left  in  darkness 
some  time  before  death,  we  find  the  internal  part  of  the  cones  long 


CHANGES  WHICH  THE  RETINA  UNDERGOES 


223 


and  filiform,  and  the  length  differs  for  different  cones  so  that  the  latter 
are  arranged  in  several  rows  quite  a  distance  from  the  limitans  externa. 
If,  on  the  contrary,  the  animal  has  been  exposed  to  light,  the  internal 
part  of  the  cones  is  shortened  and  swollen :  all  the  cones  are  placed  in  a 


A  B 

Fig.  146a.  —  Section  of  the  retina  of  a  frog.    After  Van  Genderen  Stort.   A,  in  darkness; 

B,  in  light. 

row  along  the  limitans  externa  (fig.  1460).  According  to  Van  Genderen 
Stort  the  retinal  purple  is  also  in  the  cells  of  the  pigment  epithelium,  and 
it  is  probably  secreted  by  these  cells.  He  thinks  that  the  pigment  dis- 
placement has  for  its  object  the  protection  of  the  rods  against  light, 
and  that  it  is  due  to  this  fact  that  the  epithelial  cells  send,  under  the  in- 
fluence of  light,  prolongations  between  the  rods,  almost  like  the  cells, 
called  chromatophores,  which  make  the  skin  of  some  lower  animals 
change  color  under  the  influence  of  light.  Van  Genderen  Stort  was  kind 
enough  to  make  a  present  of  some  of  his  beautiful  preparations  to  our 
laboratory.  The  phenomena  are  so  distinct  that  the  first  glance  at  the 
preparation  enables  one  to  tell  whether  the  animal  was  exposed  to  light 
or  not. 

We  must  note  further  that  Knehne  observed  certain  galvanic  phenom- 
ena dependent  on  the  action  of  light  on  the  retina. 

Bibliography.  —  Boll  (P.).  Du  Bois-Reymond?.  Archir.f.  Anat.  u.  Physiol,  1877,  p.  4. 
—  Boll  (F.).  Monatsber.  d.  Akad.  Berlin,  1877,  Jan.  11.  —  Kuehne  (W.),  in  Hermann  (L.). 
Handburh  der  Physiohgie.  Leipzig,  1879.  —  Van  Genderen  Stort.  Acad.  d1  Amsterdam,  June< 
28,  1884. 


CHAPTER   XVI. 

THE  LIGHT  SENSE 

The  functions  of  the  retina  are  divided  into  three  classes:  the  light 
sense,  the  color  sense,  and  the  form  sense. 

The  light  sense  is  the  faculty  of  recognizing  the  different  luminous 
intensities. 

100.  Psychophysical  Law  of  Fechner.  —  According  to  this  law  the 
smallest  difference  of  perceptible  illumination  is  a  constant  fraction  (about  i 
per  cent.)  of  the  total  illumination. 

Fechner  came  to  formulate  his  law  by  the  following  observation.  One 
day  he  found  a  scarcely  perceptible  difference  of  brightness  between  two 
clouds,  and  was  much  surprised  to  see  this  difference  persist  on  looking 
through  a  quite  dark  smoked  glass.  He  called  this  law  psychophysical 
because,  finding  it  also  for  other  senses,  he  was  led  to  consider  it  as  a 
general  law  of  perception.  If,  for  example,  a  line  must  have  a  length  of 
105  millimeters  in  order  that  we  can  tell  with  certainty  that  it  is  longer 
than  another  of  100  millimeters,  we  will  also  find  that  a  line  must  be  at 
least  210  millimeters  for  us  to  be  able  to  tell  with  certainty  that  it  is 
longer  than  another  of  200  millimeters.  In  both  cases  the  relation 
between  the  smallest  perceptible  difference  and  the  total  length  is  the 
same,  one-twentieth.  It  is  so  also  if  we  examine  the  smallest  perceptible 
difference  between  two  weights,  and  so  with  the  other  senses. 

We  notice  that  our  senses  differ  in  this  respect  from  most  of  our 
instruments.  With  an  ordinary  double  decimeter,  the  shortest  distance 
that  we  can  measure  (I  do  not  say  estimate)  is  a  half-millimeter;  the 
smallest  measurable  difference  between  two  lines  would  be,  therefore, 
a  half-millimeter,  and  this  whatever  may  be  the  length  of  the  lines  to 
be  measured. 

To  determine  the  ratio  between  the  smallest  difference  of  perceptible 
illumination  and  the  total  illumination,  Fechner  used  the  following  ex- 

221 


THE  LIGHT  SENSE  225 

periment  which  had  already  been  described  in  the  middle  of  the  last 
century  by  Bouguer  and  by  Lambert.  The  former  had  also  observed  the 
fact  on  which  Fcchner  later  based  his  law. 

i°  Let  us  place  at  some  distance  from  a  screen  two  candles,  A  and  B 
(fig.  147),  of  equal  intensity  I,  and  place  between  the  candles  and  the 
screen  a  stick  so  that  it  forms  two  shadows  a  and  b  on  the  screen.  The 
shadow  a  is  formed  by  A,  and  consequently  illuminated  only  by  B ;  the 


Fig.  147.  —  Experiment  of  Bouguer. 

shadow  b  receives  light  only  from  A,  and  the  remainder  of  the  screen 
receives  light  simultaneously  from  B  and  A.  By  moving  B  away  from 
the  screen,  the  shadow  b  becomes  weaker  and  weaker,  and  when  the 
distance  of  B  from  the  screen  is  nearly  ten  times  that  of  A  it  ceases  to 
be  visible. 

2°  We  replace  the  candles  by  others  of  one-half  less  intensity,  and 
repeat  the  experiment :  we  find,  as  in  the  preceding  case,  that  the  shadow 
ceases  to  be  visible  at  the  moment  when  the  distance  of  B  from  the 
screen  is  about  ten  times  that  of  A.  —  And  we  shall  find  the  same  result, 
whatever  may  be  the  intensity  of  the  candles.  —  The  law  of  Fechner  is 
thus  verified. 

Suppose  that,  in  case  i°,  at  the  moment  when  the  shadow  disappears, 
B  is  at  500  centimeters  from  the  screen,  A  at  50  centimeters.  We  know 
that  the  illumination  is  proportional  to  the  intensity  of  the  luminous 
source,  and  inversely  proportional  to  the  square  of  the  distance.  A 
gives,  therefore,  to  the  screen  an  illumination  of  &p  ,  B  an  illumination  of 
ftp  >  while  the  shadow  b  receives  an  illumination  of  pr  only.  The  differ- 
ence between  the  illumination  of  the  screen  and  that  of  the  shadow  is 
therefore : 

,1  I 

502  ^    5002 


and  the  ratio  between  this  difference  and  the  illumination  of  the  screen  is 

* 


226  PHYSIOLOGIC   OPTICS 

I 

5002  i 


_L    i    _L_          102  +  :         1Ul 
5l2  +    5002 

or  __!_,  since  the  measurement  is  not  very  exact. 
In  case  2°  the  relation  is 

1/21 

5U02 =       1 

1/2  I        1/2  I    :  =   101 
502    '"   5002 

It  is  consequently  the  same  in  both  cases. 

The  law  of  Fechner  explains  many  of  the  phenomena  daily  observed.  — 
If,  after  having  performed  with  the  candles  the  experiment  cited  above, 
we  open  the  shutters  so  that  the  daylight  strikes  the  screen,  the  shadows 
disappear.  The  difference  between  the  illumination  of  the  shadow  and 
that  of  the  screen  remains  the  same,  but  the  ratio  between  this  differ- 
ence and  the  total  illumination  of  the  screen  is  much  below  the  fraction 
of  Fechner.  —  We  read  as  well  in  the  evening,  with  a  gas  light,  as  in 
day  time,  although  the  illumination  in  day  time  is  enormously  more 
powerful,  because  the  ratio  between  the  light  reflected  by  the  black 
letters  and  that  reflected  by  the  white  paper  remains  the  same.  —  In  a 
space  illuminated  by  a  very  powerful  lamp,  the  flame  of  a  candle  held 
at  some  distance  from  the  screen  produces  a  shadow  of  it,  because  it 
absorbs  a  part  of  the  light  of  the  lamp.  If  we  move  the  candle  nearer  the 
screen,  the  illumination  increases  and  the  shadow  disappears,  although 
the  difference  of  brightness  between  it  and  the  background  remains 
the  same. 

The  law  of  Fechner  is  true  only  for  medium  degrees  of  illumination. 
If  the  illumination  becomes  very  feeble,  the  difference  must  be  relatively 
much  more  considerable.  We  read  very  well  with  a  gas  light ;  but  if  we 
lower  the  flame  much  we  cannot  read  any  longer,  although  the  ratio 
between  the  light  reflected  by  the  letters  and  that  reflected  by  the  paper 
remains  the  same.  —  It  is  possible  that  this  difference  may  be  due  to 
what  is  called  the  retina's  own  light,  an  expression  by  which  we  designate 
the  feeble  glow  which  may  still  be  perceived  in  a  completely  dark  room, 
and  which  is  due  to  internal  causes  (friction  of  the  blood  in  the  vessels 
of  the  retina  against  the  sensitive  layer,  perhaps  also  processes  in  cer- 
tain parts  of  the  brain,  etc.).  We  can  conceive  that,  if  this  light  is  added 
to  that  reflected  by  the  printed  sheet,  the  difference  of  brightness 
between  the  letters  and  the  white  sheet  may  fall  below  the  limit  of 
Fechner.  —  The  law  of  Fechner  also  ceases  to  be  applicable  when  the 


THE  LIGHT  SESSE  227 

light  is  very  strong.  This  is  why  we  cannot  see  the  spots  on  the  sun 
with  the  naked  eye,  on  account  of  the  dazzling,  but  very  well  with  a 
smoked  glass. 

But,  within  the  very  extended  limits  which  correspond  almost  to  the 
limits  of  illumination  which  we  use,  the  law  of  Fechner  is  verified  with 
very  great  exactness.  It  is  not  absolute,  however :  in  order  to  dis- 
tinguish very  fine  shades,  it  seems  that  there  is  a  certain  illumination 
which  is  most  favorable,  viz.,  that  which  approaches  the  light  of  a  clear 
day. 

The  acuity  of  the  light  sense  may  be  expressed  by  the  inverse  of  the 
fraction  of  Fechner.  If  the  latter  be  TJg- ,  we  say  that  the  acuity  of  the 
luminous  sense  is  equal  to  100;  if,  by  greatly  diminishing  the  illumina- 
tion, the  fraction  rises  to  -&-  we  say  that  the  acuity  is  only  50,  and  so 
forth. 

We  could  illustrate  the  relation  between  the  light  sense  and  the  illumi- 
nation by  a  curve  which  would  have  a  form  like  that  of  figure  148.  The 
division  of  the  horizontal  line  would  indicate  the  degree  of  illumination, 
beginning  on  the  left  by  complete  darkness,  and  terminating  on  the 


3- 


o       a,  6  ™  c-          &     «• 

Fig.  148. 

right  by  the  light  of  the  sun.  The  ordinate  of  each  point  of  the  curve 
would  measure  the  acuity  of  the  light  sense.  As  long  as  the  illumina- 
tion is  very  weak,  the  eye  sees  nothing:  when  it  reaches  a  certain  degree 
which,  in  the  figure,  is  marked  by  the  letter  a,  the  eye  begins  to  be  able 
to  distinguish  white  objects.  This  degree  of  illumination,  wrhich  forms 
the  lowest  limit  of  visibility,  is  called  threshold  ("Reizschwelle").  As  long 
as  the  illumination  remains  so  feeble,  the  light  sense  is  not  very  acute ; 
the  perceptible  differences  are  considerable.  But  the  acuity  increases 
quickly,  and  when  the  illumination  has  reached  a  certain  degree,  b,  the 
acuity  reaches  the  degree  which  it  holds  for  a  long  time,  until  the 
illumination  has  attained  the  power  c.  It  is  for  the  part  be  that  the  law 
of  Fechner  is  true,  but  not  exactly,  for  this  part  of  the  curve  is  not  alto- 
gether straight.  It  reaches  its  highest  point  at  M. 

If  we  increase  the  light  still  more,  the  luminous  sense  falls  quickly; 


228  PHYSIOLOGIC   OPTICS 

there  is  again  need  of  very  considerable  differences  of  light  in  order 
that  the  differences  may  be  distinguished. 

Let  us  designate  by  a  the  smallest  difference  of  appreciable  sensation. 
If  a  light  of  a  certain  intensity  I  produces  a  certain  sensation  S,  there  is 
need  of  an  intensity  I  +  TJ0  I  =  -}JJ-  I  to  produce  the  sensation  S  -f-  a,  an 
intensity  of  -}JJ-  I  +  -}JJ-  X  ^  =  I  (  JJJ-  )2  to  produce  the  sensation  S  +  20, 
an  intensity  of  I  (-}JJ-)8  to  produce  the  sensation  S  +  30,  and  so  forth.  It 
is  under  this  form  that  the  law  was  promulgated  by  Fechncr,  for  the 
fact  itself  was  known  since  the  works  of  Bouguer  at  the  commencement 
of  the  eighteenth  century.  The  right  by  which  we  make  the  differences 
designated  by  a  equal  to  one  another  may  be  disputed. 

101.  Measurement  of  the  Light  Sense.  —  We  usually  limit  ourselves  to 
determining: 

i°  The  threshold,  the  lowest  limit  at  which  the  eye  begins  to  distinguish 
anything  (corresponding  to  the  point  a  of  the  curve) ; 

2°  The  least  difference  of  brightness  which  we  can  distinguish  by 
ordinary  illumination,  corresponding  to  B6  or  to  Mm  (fig.  148).  It  is 
this  determination  which  we  have  just  made  with  the  candles. 

We  determine  the  threshold  (i)  with  the  photo  ptometer  of  Foerster  (fig. 
149).  It  is  a  box  painted  black  inside.  The  patient  looks  through  two 

apertures,  corresponding  to 
his  eyes  a  and  alf  towards  a 
white  surface,  placed  at  the 
far  end  of  the  box,  on  which 
are  traced  large  black  marks 
T.  The  only  light  which  can 
penetrate  into  the  box  comes 
from  a  square  window  F,  the 
aperture  of  which  we  can 
change  and  which  is  placed 
beside  the  apertures  through 
which  the  patient  looks.  Behind  the  window,  which  is  covered  with  oil 
paper,  burns  a  standard  candle  L.  The  minimum  aperture  of  the  window 
permitting  the  patient  to  see  the  black  marks  gives  the  threshold.  The 
test  is  not  very  exact ;  it  is  difficult  to  obtain  very  uniform  answers,  and 
adaptation  enormously  influences  the  result. 

The   photoptometer  of   Charpentier,   also   intended   to   determine   the 


(1)  It  is  doubtful  whether  the  determination  of  the  threshold  is  really  anything  else  than  the  deter 
initiation  of  the  fraction  of  Fechner  for  a  very  weak  illumination.  —  Theoretically,  for  the  detennina 
tion  of  the  threshold,  it  ought  to  be  required  that  the  eye  can  compare  a  very  weak  light  with  absolute 
black;  but  we  cannot  produce  absolute  black  on  account  of  the  retina's  own  light. 


THE  LIGHT  SEXSE 


229 


threshold,  consists  of  a  tube,  22  cm.  long  and  5  cm.  wide,  the  extremities 
of  which  are  closed  by  plates  of  ground  glass  A  and  B.  At  the  middle 
of  the  tube  are  placed  two  lenses  of  n  cm.  focal  distance,  and  between 
them  a  diaphragm  with  changeable  aperture.  On  illuminating  the  plate 
A  the  lenses  project  an  image  of  it  on  the  plate  B,  the  brightness  of 
which  image  we  may  cause  to  change  by  changing  the  aperture  of  the 
diaphragm.  It  is  the  plate  B  which  serves  for  the  observation ;  for  the 
protection  of  the  eye  of  the  observer  we  may  add  to  it  a  second  tube 
blackened  internally,  the  length  of  which  corresponds  to  the  distance 
for  work  of  the  observer.  An  eye-shade  which  permits  of  exact  adapta- 
tion to  the  borders  of  the  orbit  excludes  all  extraneous  light.  The 
minimum  aperture  of  the  diaphragm  which  permits  the  observer  to 
distinguish  the  plate  B,  determines  the  threshold.  —  In  every  instrument 
of  this  kind  the  difficulty  consists  especially  in  rinding  a  luminous  source 
which  can  give  a  constant  and  uniform  illumination. 

In  order  to  determine  the  smallest  perceptible  difference  we  can  use 
the  method  with  the  candles,  described  above.    Another  method  consists 


Fi^.   150  —  Disc  of  AJaxson. 

in  the  use  of  the  disc  of  Masson,  a  white  disc  of  which  sectors  of  different 
sizes  have  been  blackened  (fig.  150).  By  subjecting  this  disc  to  a  suffi- 
ciently rapid  rotation,  we  see  three  gray  rings  separated  by  white  inter- 
vals. Supposing  that  the  sector  a  is  20°,  the  sector  b  10°  and  the  sector 
c  5°,  and  supposing,  which  is  not  strictly  true,  that  the  black  does  not 
reflect  any  light  at  all,  the  brightness  of  the  three  gray  rings  would  be 
340,  350  and  355,  if  we  place  the  light  of  the  white  rings  at -360.  The 
difference  between  the  exterior  gray  rings  and  the  white  will  be  5,  and 


230 


PHYSIOLOGIC  OPTICS 


the  relation  between  this  difference  and  the  white  will  be  3^-  =  -7*-  >  which 
represents  the  value  of  the  fraction  of  Fcckner  of  the  examined  subject, 
if  he  can  distinguish  the  three  images.  If  he  can  distinguish  only  two, 
the  fraction  of  Fechner  is  —  ~0—  =  ^-,  and  so  forth.  A  great  number  of 
rings  must  be  used ;  the  illumination  must  be  good,  and  the  patient  must 
not  be  too  far  away,  in  order  to  eliminate  the  influence  of  a  diminished 
visual  acuity.  It  is  evident,  however,  that  we  cannot  completely  elimi- 
nate it;  the  acuity  may  be  so  poor  as  to  prevent  the  patient  from  dis- 
tinguishing anything. 

To  obtain  an  impression  of  a  uniform  gray  with  the  disc  of  Masson, 
it  is  necessary  that  it  rotate  with  a  certain  speed,  about  20  to  30  times 
per  second.  If  the  disc  carries  several  black  and  white  sectors,  alternat- 
ing, the  speed  may  be  less.  In  case  the  speed  is  not  sufficient,  the  disc 
gives  a  scintillating  impression  and  we  often  observe  on  it  very  beautiful 


Fig.  150a.  —  A,  Disc  of  Helmholtz;  B,  Disc  of  JBenham. 

colors.  The  disc  A  (fig.  1500)  has  been  described  by  Helmholts:  with  a 
certain  speed  the  external  ring  shows  very  vivid  colors,  among  which 
the  red  and  green  predominate;  they  are  often  arranged  in  a  manner 
which  recalls  a  series  of  short  spectra,  as  we  observe  them  with  grat- 
ings. But  the  phenomena  are  very  changeable;  in  the  second  ring, 
which  has  only  four  sectors,  the  yellow  and  blue  predominate  with  this 
speed,  but  only  to  a  slight  extent.  If  we  increase  the  speed  the  external 
ring  gives  a  uniform  gray,  while  the  second  ring  assumes  the  appearance 
which  the  external  ring  had  previously.  In  figure  1500,  B  represents  the 
disc  of  Benham.  If  we  make  it  rotate  in  the  direction  of  the  arrow,  the 
arcs  form  concentric  circles  which  present  quite  vivid  colors  in  the  fol- 
lowing order,  starting  from  the  middle:  red,  brown,  olive-green,  blue. 
Making  the  disc  rotate  in  the  opposite  direction,  the  order  of  the  colors 


THE  LIGHT  SENSE  231 

is  reversed.  The  most  beautiful  of  the  colors  is  the  red ;  the  circles  seem 
traced  in  blood. 

The  nature  of  these  phenomena  is  not  yet  elucidated.  We  must  not 
think  that  it  is  due  to  a  decomposition  of  the  white  light,  for  the  experi- 
ment succeeds  perfectly  when  illuminating  the  disc  with  homogenous 
light,  providing  it  is  sufficiently  strong.  We  even  see  colors  of  this 
kind  when  looking  towards  the  homogenous  sodium  flame. 

Another  method  of  studying  the  power  of  distinguishing  differences 
of  brightness  consists  in  examining  the  visual  acuity  for  pale  letters,  the 
brightness  of  which  we  can  determine  by  comparing  them  with  the 
rings  on  the  disc  of  Masson.  This  method,  which  was  described  by  Javal, 
was  later  developed  by  Bjerrum.  It  would  be  better  to  have  a  series  of 
tables  of  visual  acuity  with  paler  and  paler  letters,  but  generally  one 
suffices;  Bjerrum  recommended  the  use  of  letters,  the  brightness  of 
which  is  one-twelfth  weaker  than  that  of  the  background.  For  these 
letters,  a  normal  individual  has  an  acuity  of  about  one-third  the  acuity 
which  he  has  for  black  letters  on  a  white  ground.  It  is  evident  that  this 
method  cannot  be  considered  as  an  exact  measure  of  the  light  sense, 
since  the  visual  acuity  plays  a  great  part  in  the  response  of  the  patient. 
In  order  to  eliminate  to  a  certain  extent  this  influence,  one  can  use  one's 
own  eye  as  a  control,  by  lowering  his  visual  acuity  by  means  of  a  convex 
glass,  until  it  is  equal  to  that  of  the  patient. 

102.  Kesults.  —  The  threshold  of  the  normal  eye  was  determined  by 
Aubert.  He  found  that  the  weakest  light  that  we  can  distinguish  is  that 
of  a  sheet  of  white  paper  illuminated  by  a  candle  placed  at  a  distance 
of  from  200  to  250  meters.  The  threshold  varies  much  with  the  state 
of  adaptation  of  the  eye ;  placed  in  a  dark  room,  we  do  not  at  first  dis- 
tinguish objects  which  we  see  very  distinctly  later  on  when  accustomed 
to  the  darkness.  For  the  determination  of  the  threshold  it  is,  therefore, 
necessary  to  leave  the  patient  some  time  (as  much  as  20  minutes)  in  the 
darkness,  with  eyes  bandaged,  before  beginning  the  examination.  It 
seems  that,  by  this  stay  in  the  darkness,  the  entire  curve  (fig.  148)  is 
displaced  towards  the  left,  and  also  to  its  extreme  limit,  for  on  leaving 
the  darkness  the  eye  is  dazzled  by  an  illumination  which  it  usually  bears 
very  well. 

The  fraction  of  Fechner  varies  in  normal  persons  between  ~  and  -,£,- 
(0.55  to  i  per  cent.). 

For  a  very  weak  illumination,  the  light  sense  of  the  macula  is  less 
acute  than  that  of  the  surrounding  parts;  by  fixing  a  point  a  little  to 
one  side  of  it,  we  better  distinguish  objects  the  brightness  of  which 


232  PHYSIOLOGIC   OPTICS 

differs  only  slightly  from  that  of  the  background,  for  example,  when  we 
try  to  distinguish  very  dim  stars.  According  to  certain  authors,  Parinaud 
for  instance,  this  phenomenon  must  be  attributed  to  the  fact  that  the 
fovea  does  not  possess  the  faculty  of  being  able  to  adapt  itself  to  very 
weak  illuminations  like  the  rest  of  the  retina,  and  this  difference  is  ex- 
plained, because  the  fovea,  composed  of  cones,  has  no  retinal  purple, 
which  is  considered  as  the  organ  of  adaptation.  This  hypothesis  is  con- 
firmed by  another  fact,  namely,  the  knowledge  that  the  time  of  repose 
which  the  eye  requires  to  reach  complete  adaptation  is  nearly  the  same 
(about  20  minutes)  as  that  which  is  necessary  for  the  reproduction  of 
the  purple.  It  is  possible,  however,  that  the  inferiority  of  the  macula 
may  be  partly  due  to  its  yellow  pigmentation.  The  pigment  absorbs  a 
part  of  the  blue  rays,  which,  as  we  shall  see,  play  a  dominant  part  in 
vision  by  weak  illuminations. 

The  threshold  is  displaced  upwards  in  patients  suffering  from  hemera- 
lopia.  It  seems,  however,  that,  in  many  cases,  there  is  question  rather 
of  an  anomaly  of  the  adaptation,  which  requires  much  more  time  to 
take  place  than  in  the  normal  eye.  Leaving  a  person  affected  with 
hemeralopia  in  darkness,  he  continues  to  improve  for  some  time.  We 
can  prove  the  existence  of  hemeralopia  with  the  phptoptometer  of 
Foerster,  or  by  examining  the  visual  acuity  while  we  lessen  the  illumina- 
tion. Hemeralopia  is  a  constant  symptom  of  pigmentary  retinitis ;  we 
meet  it  as  often  in  cases  of  syphilitic  retinoHchoroiditis,  sometimes  in 
cases  of  detachment  of  the  retina  or  in  glaucoma.  It  is  extremely  rare 
in  cases  of  pure  atrophy  of  the  optic  nerve.  In  cases  of  idiopathic 
hemeralopia,  we  find  nothing  in  the  fundus  of  the  eye;  this  disease  is 
often  congenital  and  hereditary,  and  therefore  incurable ;  if,  on  the  con- 
trary, the  disease  has  existed  only  for  a  short  time,  its  prognosis  is 
favorable;  it  sometimes  has  an  endemic  character.  It  may  happen  that 
the  peripheral  part  of  the  visual  field  only  is  affected ;  we  then  establish 
the  existence  of  the  disease  by  examining  the  visual  field  with  a  weak 
illumination. 

We  sometimes  meet  cases  in  which  the  fraction  of  Fechner  is  in- 
creased; in  which,  consequently,  the  patients  cannot  distinguish  gray 
from  white.  This  affection  is  met  with  especially  in  cases  of  atrophy  of 
the  optic  nerve  and  in  central  scotoma.  —  One  of  the  first  cases  of  this 
kind  was  observed  at  the  clinic  of  Hansen  Grut,  at  Copenhagen,  and 
described  by  Krmchcl.  It  was  a  patient  who  presented  himself,  saying 
that  he  did  not  see  well  enough  to  find  his  way.  Examined  with  the 
ophthalmoscope,  the  papillae  were  whitish,  the  visual  acuity  was  normal, 


THE  LIGHT  SENSE  233 

and  the  visual  field  was  only  slightly  contracted.  It  was  puzzling,  there- 
fore, to  explain  the  complaints  of  the  patient  until  the  idea  of  examining 
him  with  the  disc  of  Masson  presented  itself:  the  fraction  of  Fechner 
had  increased  to  ^  .  The  patient  distinguished  perfectly  black  on  white, 
but  was  unable  to  distinguish  between  gray  shades,  as  they  present 
themselves,  for  example,  in  street  paving;  whence  the  difficulty  which 
he  experienced  finding  his  way. 

We  sometimes  meet  patients  who  claim  that  they  see  better  when  the 
illumination  is  low  (nyctalopia).  Examining  their  visual  acuity,  we  find, 
however,  that  it  does  not  increase  when  we  lessen  the  illumination  (at 
least  in  cases  in  which  we  have  not  to  do  with  a  purely  optic  phenom- 
enon :  this  is  why  a  central  leucoma  becomes  less  annoying  when  the 
pupil  is  dilated).  —  But,  on  comparing  these  persons  with  a  normal 
person,  we  note  that  by  lessening  the  illumination  the  acuity  of  the 
normal  person  diminishes  more  quickly  than  that  of  the  patient.  If  the 
normal  person  has  an  acuity  three  times  that  of  the  patient  by  ordinary 
illumination,  it  may  happen  that  on  diminishing  the  illumination  both 
would  have  the  same  visual  acuity.  Persons  suffering  from  a  central 
scotoma  sometimes  complain  of  nyctalopia  for  a  like  reason.  We  have 
seen,  indeed,  that  the  superiority  of  the  macula  over  the  rest  of  the  retina 
diminishes  with  the  illumination,  so  that  with  a  very  weak  illumination 
the  fovca  does  not  see  so  well  as  the  rest  of  the  retina.  We  can  under- 
stand, therefore,  that  a  central  scotoma  may  cause  relatively  less  annoy- 
ance when  the  illumination  is  weak. 

We  must  recall,  too,  the  quantitative  measurement  of  the  light  sense 
in  persons  affected  with  cataract.  The  patient  ought  to  be  able  to 
recognize  the  illumination  of  an  ordinary  lamp  at  a  distance  of  4  to  5 
meters,  or  that  of  a  candle  at  2  meters,  and  its  projection  must  be  good, 
that  is  to  say,  the  patient  must  be  able  to  tell  the  direction  in  which  the 
luminous  source  is  located.  If  the  patient  does  not  satisfy  these  condi- 
tions, we  may  conclude  that  there  exists  an  affection  of  the  fundus  of 
the  eye,  which  compels  us  to  make  an  unfavorable  prognosis. 

Bibliography.  —  Bonguer  (P.).  Essai  cToptique.  Paris,  1729.  —  Bouguer  (P.).  Traite 
d'optiquesur  la  gradation  de  la  lumidre.  Paris,  1760.  — Lambert  (J.  H.).  Photometria.  Augustse 
Vindelic,  1760.  —  Masson.  Etudes  de  photometric  electrique.  Ann.  de  physique  et  chimie, 
1845,  t.  XIV,  p.  129.  —  Fcerster.  Ueber  Hemeralopie  und  die  Anwendung  eines  Photometers 
im  Gebi'te  der  Ophthalmologie.  Breslau,  1857.  —  Fechner.  Elemente  der  Psychophysik.  Leip- 
zig, 1860,  2  vol.  — Klein.  De  V influence  de  Vedairage  sur  Vacuite  visuelle.  Paris,  187;-5.  — 
Krenchel  (V).  in  Klin.  Monatsbl.fur  Augenheiik.  February,  1880.  —  Bjerrum  (J.).  Under. -(r- 
gelsen  of  Synet.  (Danish).  Copenhagen,  1894.  Cbarpentier  (A.)  La  lumiere  et  lescoulevr*. 
Paris,  Baillere,  1888. 

The  work  of  Lambert  is  first  in  importance.  A  German  translation  with  notes  by  Anding, 
has  just  appeared  at  W.  Ostwald.  Die  Klassiker  der  exakten  Wissentchaften.  Leipzig,  1892. 


CHAPTER  XVII. 

THE  COLOR  SENSE. 

103.  General  Eemarks.  —  On  analyzing  any  color  with  the  spectro- 
scope, we  find  no  other  tints  than  those  which  compose  the  solar  spec- 
trum, mixed  in  different  proportions.  The  only  colors  which  would 
seem  to  form  an  exception,  the  brownish  colors,  are  really  red  and 
yellow  colors  of  slight  intensity,  more  or  less  mixed  with  white.  To 
examine  the  color  sense,  therefore,  we  may  limit  ourselves  to  the  study 
of  spectral  colors  and  their  mixtures.  We  have  thus  the  advantage  of 
experimenting  with  pure  colors,  which  are  easily  definable  by  the  wave 
length  of  the  rays.  The  use  of  colored  papers,  although  very  convenient, 
has  many  drawbacks,  in  consequence  of  the  impossibility  of  defining 
exactly  the  color  of  the  paper  used,  so  that  another  experimenter  may 
be  able  to  procure  a  similar  tint.  On  the  contrary,  if  we  obtain  a  result 
with  spectral  light  of  a  certain  wave  length,  the  experiment  may  be 
described  in  a  very  exact  manner,  the  only  condition  which  may  be  left 
uncertain  being  the  intensity  of  the  light  used.  On  analyzing  blue  spec- 
tral light  with  the  spectroscope  we  find  only  blue,  while  the  light  reflected 
by  a  paper  of  this  color  contains,  besides  blue,  most  of  the  other  colors 
of  the  spectrum.  There  is  another  way  of  procuring  pure  colors,  for 
the  incandescent  vapors  give  monochromatic  light,  at  least  approxi- 
mately. Thus  the  sodium  flame  gives  yellow  light  of  a  wave  length  of 
0.59  /Jt,  the  lithium  flames  red  light  (0.67  /*),  the  thallium  flame  green 
light  (0.54  ,u),  and  the  strontium  flame  blue  light  (0.46  /^).  But,  as  a  rule, 
these  flames  are  in  less  common  use  than  spectral  light.  The  light  which 
passes  through  colored  glasses  is  generally  far  from  being  monochro- 
matic ;  we  must,  however,  except  red  glasses,  colored  with  oxide  of 
copper,  which,  when  they  are  a  little  dark,  allow  scarcely  any  but  red 
rays  to  pass.  Among  liquids  we  sometimes  use  the  solution  of  bi- 
chromate of  potash,  which  absorbs  the  blue  extremity  of  the  spectrum, 
and  the  solution  of  sulphate  of  copper-ammoniac,  which  absorbs  the  red, 

234 


THE   COLOR  SENSE 


235 


the  yellow  and  part  of  the  green.    A  mixture  of  both  allows  a  quite  pure 
green  light  to  pass. 


1 

3     ( 

• 

I 

)                     E 

:               i 

( 

I                                           H 

i 

70 

1  1  1 

60 

Mill 

1    I   1   1    1    t 

i  il  . 

1       1       1        1         i 

,      ,    -1 

^_. 

A^_ 

_^ 

\  JA^ 

A^ 

..  -^-  .^~ 

J\^                                       J 

Red 


Orange        Yellow          Green 


Blue 


Indigo 


Violet 


H 


H 


0 

1  1  1  1  r 

1  1  1 

eol 
1    1     1    1     1     1 

1     i    t    1    I 

,  ,"1  i 

I     1    t    1    I 

i  i  ,1 

, 

Red 


Orange 


Yellow 


Green 


Blue       Indigo        Violet 


Fig.  151. — I.  Spectrum  of  refraction. — II.  Spectrum  of  diffraction. 
The  numbers  indicate  the  wave  length  in  hundredths  of  p. 


We  distinguish  between  the  spectra  of  refraction,  formed  by  means  of 
prisms,  and  the  spectra  of  diffraction,  which  are  obtained  by  allowing 
light  to  pass  through  a  grating,  that  is  to  say,  a  glass  plate  on  which  a 
great  number  of  very  fine  parallel  lines  have  been  traced. 

The  spectra  of  refraction  are  preferable  because  they  are,  generally, 
purer  than  the  spectra  of  diffraction.  They  have  this  inconvenience  that 
the  relative  width  of  the  different  colors  varies  with  the  prism  used. 
The  red  and  orange  colors  are  reduced  to  a  relatively  small  space,  while 
the  blue  and  violet  colors  are  stretched  out  over  a  large  surface.  In 
the  spectrum  of  diffraction,  the  distance  between  the  different  colors  is, 
on  the  contrary,  proportional  to  the  difference  of  the  wave  length  (fig. 
151),  so  that  all  the  spectra  of  diffraction  are  alike  and  form,  so  to  speak, 
the  normal  spectrum.  The  yellow  is  at  the  middle  of  the  spectrum ;  the 
red  and  orange  occupy  half,  the  green,  blue,  indigo  and  violet  the  other 
half. 

As  landmarks  in  the  spectrum,  we  frequently  use  the  lines  of  Fraun- 
hofcr,  the  wave  lengths  of  which  have  been  very  exactly  determined.  Say, 


236  PHYSIOLOGIC   OPTICS 

for  example,  that  the  rays,  which  we  use,  are  situated  at  half  the  distance 
between  E  and  F;  on  the  scale  of  figure  151  we  see  that  the  light  used 
must  have  had  a  wave  length  of  0.50  to  0.51  /*  .  —  It  is  better,  however, 
to  determine  the  wave  length  directly,  which  is  easily  done  by  means  of 
a  grating. 

I  have  already  observed  that  there  are  in  the  spectrum  rays  beyond 
the  red  which  are  not  visible.  The  extreme  visible  red  corresponds 
nearly  to  a  wave  length  of  0.8  //.  The  colors  then  follow  in  the  well- 
known  order :  red,  orange,  yellow,  green,  blue,  indigo,  violet.  Beyond 
the  violet  come  ultra-violet  rays,  which  are  not  visible  under  ordinary 
conditions,  but  which  can  be  observed  by  means  of  a  photographic  plate, 
or  by  receiving  them  on  a  fluorescent  screen,  or  simply  by  eliminating  all 
other  light  according  to  the  method  given  on  page  109.  They  are  then 
seen  with  a  certain  grayish  color,  which  is,  perhaps,  partly  due  to  the 
fact  that  the  retina  is  fluorescent. 

We  distinguish  colors  according  to  their  hue  (ton),  their  purity  or  tint 
(saturation)  and  their  brightness  or  shade  (intensite).  The  tone  or  hue  de- 
pends on  the  wave  length  alone,  or,  in  other  words,  on  the  position  of 
the  color  in  the  spectrum :  the  red  has  a  different  hue  from  the  green, 
etc.  The  saturation  or  purity  depends  on  the  white  which  is  found  added 
to  nearly  all  existing  colors,  except  those  of  the  spectrum:  the  less 
white  there  is,  the  greater  the  purity  of  the  color.  The  intensity  or  bright- 
ness depends  on  the  quantity  of  light.  If  we  have  formed  a  spectrum  by 
means  of  a  certain  luminous  source,  and  then  increase  the  intensity  of 
this  source,  the  intensity  of  all  the  colors  of  the  spectrum  increases  at 
the  same  time. 

The  hue  changes  constantly  in  the  spectrum :  that  is  to  say,  if  we  take 
light  from  two  different  parts  of  the  spectrum,  we  cannot  make  them 
alike  by  changing  their  brightness.  The  change  reaches  its  greatest 
rapidity  in  the  green-blue  part  of  the  spectrum,  where  even  a  variation 
in  the  wave  length  of  o.ooi  /*  produces  a  change  of  hue;  the  rapidity 
diminishes  towards  the  extremity,  and  in  the  extreme  parts  of  the  red 
and  violet  the  hue  remains  the  same  (Kocnig  and  Dieterici).  —  According 
to  Kcenig  we  can  distinguish  about  160  different  hues  in  the  spectrum. 
On  the  other  hand,  according  to  the  same  author,  the  eye  can  distinguish 
about  600  different  degrees  of  brightness  between  the  threshold  and 
dazzling  light.  This  is  true  for  white  and  probably  also  for  the  different 
hues  of  the  spectrum,  but  the  total  number  of  different  impressions 
between  which  the  eye  can  make  a  distinction  is,  however,  less  than  one 
would  think  in  view  of  these  indications,  for  when  the  brightness  be- 


THE  COLOR  SENSE 


237 


comes  very  great  or  very  feeble,  the  color  disappears  as  we -shall  see 
forthwith. 

On  examining  the  spectrum  it  is  easy  to  see  that  our  sensations  of  colors 
form  a  continuous  series.  We  begin  with  the  red,  which  passes  from 
orange  to  yellow,  etc.,  and  end  with  the  violet,  the  tint  of  which  presents 
an  analogy  to  the  red.  The  intermediary  color  between  the  red  and 
violet,  purple,  is  not  found  in  the  spectrum,  but  it  would  be  possible  that 


Greeu 


Yellowish -Green 


Bluish-Green 


Yellc 


Blue 


Violet 


Purple 
Fig.   1.V2.  —  Table  of  colors  after  Newton. 


this  color  would  be  produced  by  ultra-violet  rays  if  the  retina  were  not 
fluorescent. 

We  can,  therefore,  represent  the  gamut  of  the  colors  by  a  closed 
curve.  The  simplest  form  we  can  give  to  this  curve  is  that  of  a  circle 
(fig.  152),  replacing,  however,  the  part  corresponding  to  the  purple  by 
a  straight  line ;  we  shall  soon  see  why.  We  suppose  all  the  colors  of  the 
spectrum  placed  on  this  circle  in  their  natural  order.  At  the  center  is 
the  white,  and  on  the  right,  going  from  the  white  to  one  of  the  spectral 
colors,  are  the  different  tints,  the  purity  being  greater  as  we  approach 
the  spectral  color.  If  we  mix  two  colors,  the  mixture  will  have  one  of 
the  intermediary  hues  often  bleached  with  white,  and  if  we  mix,  in  suit- 
able proportions,  two  colors  situated  opposite  to  each  other  on  the  table, 


238  PHYSIOLOGIC  OPTICS 

we  obtain  pure  white.  Two  colors  which,  when  mixed,  give  white,  are 
called  complementary.  For  this  reason  red  is  complementary  to  green- 
blue,  green  to  purple,  yellow  to  indigo  and  orange  to  blue. 

It  was  Newton  who  first  arranged  the  colors  as  in  this  table.  We  find 
in  it  all  hues  and  all  degrees  of  purity. 

I  must  add  a  few  words  on  the  sensation  of  black.  First,  it  must  be 
noted  that  black  produces  a  real  sensation :  to  see  black  is  not  the  same 
thing  as  to  see  nothing  at  all.  The  most  striking  example  is  that  of  the 
spot  of  Mariotte,  which  corresponds  to  the  papilla.  In  this  spot  we  see 
nothing,  but  we  do  not  see  it  black.  By  looking  directly  in  front,  one 
sees  a  part  of  the  space  in  which  one  is;  in  regard  to  that  which  is 
beyond  the  limits  of  the  visual  field,  one  does  not  see  it,  but  it  does  not 
appear  black.  The  impression  of  black  is,  therefore,  a  true  sensation, 
which  corresponds  to  the  state  of  repose  of  the  visual  organ. 

There  exists  no  completely  black  object  in  nature:  even  black  velvets 
still  reflect  a  comparatively  considerable  quantity  of  light.  A  black 
object  placed  in  the  direct  light  of  the  sun  may  appear  clearer  than  a 
white  object  placed  in  the  shadow. 

According  to  some  measurements  which  I  have  made,  the  whitest 
paper  which  I  could  find  (visiting  cards)  returns  only  about  a  third  of 
the  incident  light  (37  per  cent.).  The  normal  white  of  Kcenig,  which  is 
obtained  by  burning  a  thread  of  magnesium  and  allowing  the  vapor  to 
be  deposited  on  a  sheet  of  paper,  sends  back  about  two-thirds  of  the 
light ;  its  whiteness  is  nearly  that  of  snow.  Ordinary  black  paper  (bristol 
black)  returns  nearly  5  per  cent,  of  the  incident  light  (1.5  per  cent,  of  the 
quantity  reflected  by  the  white  paper) ;  black  velvety  paper  sends  back 
about  5  per  1000  of  the  incident  light  (1.5  per  1000  the  quantity  reflected 
by  white  paper).  The  most  absolute  black  that  we  can  produce  is  that 
of  an  aperture  made  in  the  side  of  a  closed  box,  blackened  internally. 
Compared  with  this  black  even  the  velvety  paper  appears  slightly 
grayish. 

Black  does  not  figure  on  the  table  of  Newton.  If  we  desire  to  include 
it  in  the  illustration,  we  must  suppose  the  colors  placed  on  a  body  of 
three  dimensions,  a  pyramid  or  a  cone  (Lambert).  The  table  of  Newton 
would  form  the  base  of  the  cone,  while  the  black  would  form  its  apex  : 
on  the  conical  surface  we  would  place  the  colors  of  little  intensity.  Thus 
the  brown  would  be  placed  between  the  yellow  and  the  black,  etc. 


104.  Phenomena  of  Contrast  (Simultaneous).  —  Our  judgment  of  colors 
is  always  influenced  by  the  colors  of  surrounding  objects.   This  fact  is 


THE  COLOR  SENSE 


239 


well  known  to  painters,  whose  color  sense  is  generally  highly  developed, 
so  that  they  often  see  colors  that  inexperienced  persons  would  not  per- 
ceive. But,  in  special  circumstances,  this  influence  makes  itself  felt  in 
a  very  striking  manner. 

i°  EXPERIMENT  OF  H.  MEYER.  —  Placing  a  small  piece  of  gray  paper 
on  a  sheet  of  colored  paper  and  covering  the  whole  with  a  sheet  of  tissue 
paper,  the  small  piece  is  seen  to  be  of  the  complementary  color.  Pfluger 
had  letters,  thus  arranged,  printed  for  the  examination  of  color-blind- 
ness. 

2°  EXPERIMENT  OF  RAGONA  SCINA.  —  Two  sheets  of  white  cardboard 
(BC  and  BD,  fig.  153)  are  placed  so  as  to  form  between  them  a  right 

angle ;  on  each  is  a  black  spot,  a,  b,  and 
a  red  glass  BE  is  placed  so  as  to  form 
an  angle  of  45  degrees  with  the  card- 
board. The  eye  A  receives  from  BC  the 
rays  which  have  passed  through  the  red 
glass  and  from  BD  the  rays  reflected  by 
this  glass.  The  former  are  red,  the  latter 
white,  so  that  the  background  BC  would 
appear  whitish-red.  The  spot  a  is  seen  at 
a'  of  a  deep  red  color,  because  the  eye 
receives  at  this  place  only  red  rays,  the 
white  rays  which  should  come  from  BD 
being  wanting.  Corresponding  to  b  the 
eye  receives  only  white  rays  coming 
from  BD,  and  nevertheless,  b  appears  of 
an  intense  green  by  contrast.  The  ex- 
periment, which  is  very  pretty,  may  be 
performed  with  other  colored  glasses. 
We  always  see  a'  and  b  in  complemen- 
tary colors. 


Fig.  153. 
Experiment  of  Ragona  Scina. 


3°  COLORED  SHADOWS.  —  Let  A  and  B  (fig.  154)  be  two  candles,  of 
which  A  may  be  the  brighter ;  in  front  of  A  we  place  a  red  glass ;  a  and  b 
are  the  shadows  which  the  stick  c  forms  on  a  white  screen.  The  screen 
illuminated  by  the  white  light  from  B  and  the  red  light  from  A,  should 
appear  whitish-red,  but  the  red  is  scarcely  perceptible ;  b,  which  is  illumi- 
nated only  by  the  red  light  from  A,  appears  red,  and  a,  which  should 
appear  white,  appears  green,  by  contrast.  We  can  also  make  the  ex- 
periment with  daylight  and  that  of  a  candle,  in  which  case  there  is  no 


240  PHYSIOLOGIC   OPTICS 

need  of  the  colored  glass,  since  the  colors  of  the «, 

two  lights  already  differ.    We  begin  by  illuminat- 
ing the  screen  with  daylight;  we  see  the  screen  ^ 
white  and  the  shadow  black  (gray).     On  lighting 
the  candle  the  screen  still  appears  white,  although                 / 
it  would  seem  that  it  ought  to  appear  yellow,  since              / 
it  is  partly  illuminated  by  the  yellow  light  of  the           / 
candle;   the   shadow,  which  just  now  appeared         rj B 
gray,  has  become  yellow  by  the  illumination  of               Fig.  154. 

the  candle,  and  the  other  shadow,  which  receives    Experiment  with  colored 

,,  shadows, 

the  daylight,  appears  blue    by  contrast. 

4°  EXPERIMENT  OF  DOVE.  —  Analogous  phenomena  with  colored 
shadows  are  observed  when  we  place  a  colored  glass  opposite  a  mirror. 
We  then  see  two  images  of  a  white  object,  one  by  reflection  on  the  an- 
terior surface  of  the  glass,  the  other  by  reflection  on  the  mirror;  this 
latter  has  the  color  of  the  glass,  since  the  rays  have  passed  through  the 
.glass  twice.  The  first,  which  ought  to  be  white,  shows  by  contrast  the 
complementary  color.  With  a  black  object  on  a  white  ground,  the  sash 
of  a  window  for  example,  we  have  the  phenomena  reversed. 

We  observe  that  the  expression  "by  contrast"  scarcely  explains  these 
.singular  phenomena.  In  most  of  these  cases  it  seems  that  the  funda- 
mental phenomenon  lies  in  the  defectiveness  of  our  judgment  of  white. 
Thomas  Young  already  directed  attention  to  the  fact  that  a  sheet  of  white 
paper  appears  white  to  us,  as  well  when  illuminated  by  the  yellow  light 
of  a  candle  as  by  the  red  light  of  a  coal  fire.  We  may  say  that  we  con- 
sider always  as  white  the  bodies  which  return  the  greatest  quantity  of 
light,  whatever  may  be  the  light  used  (Javal).  This  is  primarily  inde- 
pendent of  the  illumination,  and  this  is  why  a  sheet  of  white  paper  ap- 
pears to  us  white  with  different  illuminations.  But  the  recollection  of  the 
illumination  by  daylight  plays,  nevertheless,  a  part,  so  that,  if  the  real 
color  differs  much  from  it,  the  paper  seems  white  with  a  slight  colored 
tone :  thus  when  we  look  at  it  through  a  red  glass,  in  which  case  the 
paper  returns  red  rays  only,  it  appears  a  reddish-white. 

In  the  experiment  with  colored  shadows  the  screen  appears  to  us 
white  when  it  is  illuminated  by  daylight  only,  and  also  when  it  is  illumi- 
nated by  a  mixture  of  daylight  and  candle  light  at  the  same  time.  But 
if,  under  these  circumstances,  the  whitish-yellow  light  which  illuminates 
the  screen  appears  white  to  us,  it  is  not  strange  that  the  white  light  which 
illuminates  one  of  the  shadows  appears  blue,  that  is  to  say,  less  yellow 


THE  COLOR  SENSE 


241 


than  the  screen.  We  may  regard,  so  to  speak,  the  zero  of  the  scale  of 
our  color  sensations  (the  white)  displaced,  and  with  it  the  entire  scale. 
TRUE  SIMULTANEOUS  CONTRAST.  —  While  the  phenomena  of  which 
we  have  just  spoken  are  due  to  a  false  judgment  of  the  color  white, 
there  are  others  which  are  due  to  a  true  contrast.  By  making  a  disc 
like  that  of  figure  155,  but  having  a  greater  number  of  sectors,  rotate 
we  obtain  gray  rings,  and  we  observe  that  we  cannot  see  the  outer  rings 
which  are  very  pale ;  we  see  only  the  borders  of  each  ring :  the  external 
border,  which  appears  deeper  than  the  rest  of  the  ring,  by  contrast  with 


Fig.  155.  —  Disc  of  Masson. 

the  following  ring  which  is  paler,  and  the  internal  border  which  appears 
paler  than  the  rest,  by  contrast  with  the  neighboring  darker  ring.  By 
replacing  the  white  and  black  by  yellow  and  blue,  we  obtain  rings  which 
present  different  shades  of  gray;  the  internal  rings  are  bluish,  the  ex- 
ternal rings  yellowish.  But  each  ring  has  an  internal  border  which  is 
yellow,  by  contrast  with  the  preceding  ring  which  is  bluer,  and  an  ex- 
ternal border  which  is  blue,  by  contrast  with  the  following  ring  which 
is  yellower.  The  phenomenon  is  very  pronounced,  but  disappears,  at 
least  in  a  great  part,  if  we  separate  the  rings  by  very  fine  black  circles. 
The  diffuse  borders  favor  considerably  the  effect  of  the  contrast. 

105.  After-images  (Successive  Contrast).  —  When  we  look  at  a  small 
colored  surface,  placed  on  a  white  ground,  by  fixing  exactly  the  same 
point  for  a  short  time,  we  observe  that  the  color  diminishes  gradually 
in  brightness:  the  red  becomes  brown,  etc.  We  observe  at  the  same 
time  that  the  object  is  surrounded  by  a  narrow  border  of  the  comple- 


242  PHYSIOLOGIC   OPTICS 

mentary  color,  due  to  the  fact  that,  in  spite  of  himself,  the  observer 
makes  slight  changes  in  the  direction  of  the  look.  We  explain  the 
phenomenon  by  saying  that  the  part  of  the  retina  where  the  image  is 
formed  is  fatigued  for  the  color  in  question.  If  we  then  transfer  the 
look  to  a  sheet  of  white  paper,  we  see  an  image  tinted  with  the  comple- 
mentary color.  If  the  surface  be  red,  the  image  appears  bluish-green. 
We  may  suppose  the  white  color  as  composed  of  two  complementary 
colors,  red  and  green ;  the  retina  being  fatigued  for  the  red  color,  it  is 
the  green  color  which  predominates.  If  the  object  we  look  at  is  white, 
the  after-image  is  black;  but  if  we  look  at  a  flame  or  other  very 
bright  object,  we  obtain  a  colored  after-image,  the  color  of  which 
changes  before  its  disappearance. 

The  after-images  of  the  complementary  color  are  called  negative: 
we  can  also  obtain  positive  images,  each  part  of  which  has  the  same  color 
as  the  original.  We  close  the  eyes  and  cover  them  with  the  hand  for 
some  minutes,  so  that  no  light  can  enter  the  eye.  We  keep  in  this  posi- 
tion for  some  time  until  all  prior  impressions  .on  the  retina  have  dis- 
appeared. This  done,  we  remove  the  hand  and  open  the  eyes  for  an 
instant,  without,  however,  changing  the  direction  of  the  look,  shut  them 
immediately  and  cover  them  again.  If  the  experiment  is  very  successful, 
we  then  see  a  positive  image  of  exterior  objects,  of  a  surprising  dis- 
tinctness. We  can  scarcely  believe  that  we  have  really  closed  our  eyes ; 
the  hand  seems  transparent.  If  we  continue  to  keep  the  eyes  closed,  we 
see  the  less  illuminated  parts  of  the  image  disappear,  while  the  more 
illuminated  parts  change  color,  becoming  bluish,  violet,  orange,  etc. ; 
the  image  disappears  and  returns  again,  and  so  forth. 

A  clear  after-image  of  a  chess-board,  or  other  analogous  figure, 
shows  phenomena  exactly  like  those  which  I  shall  describe  later  under 
the  heading  "Phenomenon  of  Tro.vler."  It  now  becomes  probable  that 
the  disappearance  and  reappearance  of  the  after-images  are  due 
to  the  same  causes,  likewise  unknown,  as  this  phenomenon.  The 
after-images,  of  which  I  have  just  spoken,  last  for  a  relatively  long 
time,  but  there  are  others  which  last  so  short  a  time  that  they  escape 
observation  in  the  ordinary  distances  of  life.  The  simplest  way  of  mak- 
ing them  appear  consists  in  moving  the  object  which  is  intended  to 
produce  them.  The  secondary  image  then  seems  to  follow  the  object 
because  it  is  formed  at  the  place  where  the  object  was  a  moment  before, 
and  because  it  lasts  only  an  instant.  Ordinary  after-images  form, 
in  these  circumstances,  a  long  luminous  series.  The  most  striking  of 
these  phenomena  was  described  by  Purkinje  and  later,  under  the  name  of 


THE  COLOR  SENSE  243 

"recurrent  vision,"  by  Davis.  The  experiment  is  very  easy  to  perform : 
we  light  a  match  in  darkness,  blow  out  the  flame  and  move  the  burning 
wood  around.  We  shall  then  see  the  blue  after-image,  feebly  lumin- 
ous but  bright  nevertheless,  follow  the  match  at  some  distance,  repro- 
ducing its  form  exactly.  There  are  two  conditions  necessary  to  the 
success  of  the  experiment :  one  is  that  we  do  not  follow  the  match 
with  the  look,  for  the  phenomenon  is  visible  only  in  indirect  vision ; 
the  other  is  that  we  use  the  proper  speed,  neither  too  fast  nor  too  slow. 
With  a  certain  rate  of  speed  the  image  (called  "ghost"  by  English 
writers)  seems  double.  According  to  Bidwell  the  interval  between  the 
match  and  the  after-image  corresponds  to  almost  one-fifth  of  a  second. 
This  author  sees  the  space  between  the  match  and  the  remainder  of 
the  field  blacker,  an  observation  which  was  confirmed  by  Agaboban,  who 
repeated  the  experiment  at  the  Sorbonne,  but  I  have  not  been  able  to 
verify  it. 

By  making  a  black  disc  with  a  white  sector  rotate  in  full  sunlight 
Charpenticr  observed  a  black  sector  which  formed  in  the  white  sector 
not  far  from  its  anterior  border,  and  which  was  sometimes  followed  by 
several  others  less  pronounced.  At  times  the  interval  between  the  an- 
terior border  of  the  white  sector  and  that  of  the  black  sector  corre- 
sponded to  about  -ft-  of  a  second.  The  observation  indicates  that  when 
we  allow  an  illumination  to  act  for  a  very  short  period  on  the  retina  the 
latter  becomes  insensible  to  it  after  a  sixtieth  of  a  second  to  reacquire 
its  sensibility  after  the  lapse  of  the  same  period ;  sometimes  the  phenom- 
enon is  repeated  several  times  (retinal  oscillations).  The  phenomenon 
must  not  be  confounded  with  "recurrent  vision"  for  which  the  interval 
is  much  longer. 

106.  Phenomena  Dependent  on  the  Variation  of  the  Brightness  of  the 
Colors.  —  The  brightnesses  of  two  sources  of  light  of  the  same  color  are 
compared  as  easily  as  if  there  was  a  question  of  white  light,  and  we  find 
almost  the  same  value  for  the  fraction  of  Fechner.  If  we  attempt  to 
compare  lights  of  different  color  the  eye  manifests,  on  the  contrary,  a 
very  great  uncertainty,  and  besides  we  encounter  a  difficulty  caused  by 
what  is  called  the  phenomenon  of  Purkinje.  Suppose  that  we  have  two 
sources  of  white  light,  which  we  have  found  of  equal  brightness.  If 
then  we  diminish  the  intensity  of  both  one-half  we  shall  find  them  again 
equal.  But  if  we  equalize  two  sources,  one  of  which  is  blue  and  the 
other  red,  and  that  then  we  diminish  their  brightness  one-half,  the  blue 
light  will  appear  much  brighter  than  the  red  light.  —  Let  us  select  two 


244  PHYSIOLOGIC  OPTICS 

papers,  one  red  and  one  blue,  which  by  daylight  illumination  appear  to 
have  the  same  brightness ;  by  diminishing  the  illumination  the  blue  paper 
will  appear  brighter  than  the  red  paper.  With  a  very  feeble  illumination 
the  red  paper  will  appear  black,  the  blue  paper  a  pale  gray.  In  order 
that  the  experiment  may  succeed  well  the  papers  must  be  seen  under  an 
angle  which  is  not  too  small,  for  the  phenomenon  is  but  slightly  pro- 
nounced for  the  macula.  In  accordance  with  these  observations  Mace 
de  Lepinay  and  Nicati  have  shown  that  the  visual  acuity  falls  much  more 
quickly  on  diminishing  the  illumination  when  we  use  red  light  than  when 
we  use  blue  light :  we  select  a  red  glass  and  a  blue  glass  so  that  we  may 
have,  by  daylight  illumination,  the  same  acuity  on  looking  at  the  chart 
through  either.  If  then  we  close  the  shutters  almost  completely  so  as 
to  greatly  diminish  the  illumination,  we  observe  that  the  blue  glass 
enables  us  to  still  read  half  of  the  chart,  while  with  the  red  glass  we 
cannot,  at  the  first  moment,  distinguish  even  the  chart;  after  a  little 
while  we  can  read  the  large  letters,  but  the  acuity  for  the  red  always 
remains  lower  than  the  acuity  for  the  blue  which  is  stationary.  Kocnig 
and  Brodhun  also  have  shown  that  the  increase  of  the  fraction  of  Fechner, 
at  the  lower  limit,  begins  sooner  for  the  red  than  for  the  blue. 

The  following  experiment  shows  in  a  very  striking  manner  the  differ- 
ence which  exists  in  this  regard  between  the  two  extremities  of  the 
spectrum.  We  project  the  spectrum  on  a  screen  A,  pierced  by  two 
apertures,  allowing  the  red  rays  and  the  blue  and  violet  rays  to  pass. 
Behind  the  screen  A  we  place  a  lens  which  reunites  these  rays  on  a 
second  screen  B,  forming  on  it  an  image  of  the  surface  of  the  prism 
which  is  turned  towards  A.  This  image  then  shows  a  pretty,  purple 
color.  In  front  of  the  screen  B  we  place  a  stick  which  forms  thereon 
two  shadows,  one  red,  the  other  blue,  and  it  is  easy  to  so  regulate  the 
apertures  of  the  screen  A  that  both  shadows  may  have  the  same 
brightness.  If  we  now  diminish  the  width  of  the  slit  through  which  light 
reaches  the  prism  the  purple  is  diluted  more  and  more  with  white.  The 
blue  shadow  becomes  grayish,  and  brighter  and  brighter  compared  with 
the  background,  while  the  red  shadow  retains  its  color,  but  becomes 
darker  and  darker.  Finally  it  is  nearly  black  and  alone  visible,  the  other 
shadow  being  gray  and  having  nearly  the  same  brightness  as  the  back- 
ground. 

In  the  spectrum  it  is  the  yellow  and  green  rays  which  have  most 
brightness.  The  brightness  diminishes  towards  the  two  extremities  of 
the  spectrum,  but  more  towards  the  blue  extremity  than  towards  the 
red  extremity.  We  must  note,  however,  that  if  the  blue  and  violet  colors 


THE  COLOR  SEXSE  245 

seem  relatively  feeble  in  the  prismatic  spectrum,  this  is  partly  due  to 
the  fact  that  these  colors  are  spread  over  a  much  greater  space  than  the 
others.  In  the  spectrum  of  diffraction  the  intensity  is  greatest  in  the 
middle  of  the  spectrum,  and  diminishes  almost  alike  towards  the  two 
extremities. 

If  we  lessen  the  intensity  of  the  luminous  source  the  colors  of  the 
spectrum  change  hue.  We  first  see  the  yellow  and  blue  colors  disappear ; 
there  remain  only  the  red,  green  and  violet,  which  take  the  place  of  the 
colors  which  have  disappeared.  On  still  further  diminishing  the  bright- 
ness, the  blue  changes  into  a  blue-gray,  the  green  into  a  green-gray,  the 
red  becomes  brownish  and  finally  all  the  colors  disappear,  and  we  see 
only  gray.  The  red  alone  forms  an  exception;  it  does  not  seem  to 
change  into  gray  before  disappearing. 

There  exists  a  very  pretty  method  of  showing  the  change  of  appear- 
ance of  the  spectrum  by  the  diminution  of  the  brightness.  It  consists 
in  gluing  a  board  of  velvety  black  paper  on  a  white  screen  so  that  by 
projecting  on  it  a  horizontal  spectrum  the  upper  half  is  formed  on  the 
black  paper  and  the  lower  half  on  the  white  screen.  This  latter  half 
shows  the  spectrum  as  it  ordinarily  appears,  while  the  upper  half  has 
the  form  of  a  gray  band,  with  the  exception  of  the  part  corresponding 
to  the  red  which  appears  brown. 

The  colors  disappear,  therefore,  when  the  brightness  of  the  rays  be- 
comes very  feeble.  Also  when  the  brightness  becomes  very  strong  the 
impression  approaches  white.  The  sun,  seen  through  a  red  glass,  ap- 
pears a  whitish-yellow,  although  the  glass  allows  only  red  rays  to  pass. 
Concentrating  the  light  of  the  sun  on  a  sheet  of  white  paper  with  a  lens, 
after  having  made  it  pass  through  a  blue  glass,  the  image  of  the  sun 
appears  white.  When  we  look  at  the  sun  through  a  prism  the  spectrum 
presents  itself  as  a  colorless  strip  of  a  dazzling  brightness.  Here  also 
it  is  the  red  which  best  maintains  its  color;  in  most  cases  it  appears  a 
whitish-yellow. 

According  to  Parinaud,  these  phenomena  depend  on  the  adaptation 
of  the  eye.  The  spectrum  of  feeble  brightness,  which  appears  gray  to 
the  adapted  eye,  is  invisible  to  the  eye  not  adapted,  and  when,  the  in- 
tensity increasing,  it  becomes  visible  to  the  non-adapted  eye  it  in  turn 
appears  colored.  Parinaud  determined  the  threshold  for  different  rays 
of  the  spectrum,  and  found  the  curves  represented  by  figure  156.  The 
upper  curve  is  that  of  the  adapted  eye,  the  lower  curve  that  of  the  eye  not 
adapted.  The  different  parts  of  the  spectrum  are  indicated  by  the  ver- 
tical lines,  prolongations  of  the  lines  of  Fraunhofer  in  the  diagram  of  the 


246 


PHYSIOLOGIC   OPTICS 


spectrum  which  is  above  the  figure.  The  numbers  on  the  left  indicate 
the  quantities  of  light  necessary  in  order  that  these  different  parts  of  the 
spectrum  may  be  perceived.  Thus  the  adapted  eye  requires  a  quantity 
of  light  equal  to  I  (this  quantity  being  taken  as  the  unit)  in  order  to 


A      B    C          D  E  F 


100 
200 
300 


Fig.  156.  —  After  Parinaud. 


perceive  the  green  rays  near  E,  while  the  non-adapted  eye  requires  a 
quantity  equal  to  100  in  order  to  perceive  the  same  rays,  and  a  quantity 
equal  to  1500  to  perceive  the  blue  rays  near  G.  We  see  that  the  eye,  by 
adaptation,  gains  nothing  for  the  perception  of  red  rays,  whilst  it  gains 
enormously  for  the  more  refrangible  rays.  But  it  gains  only  in  luminous 
sensibility :  except  the  part  be,  which  is  common  to  the  two  curves,  the 
whole  upper  curve  corresponds  to  colorless  sensations  only.  According 


THE  COLOR  SENSE  247 

to  Parinaitd,  the  fovea  gains  nothing  by  adaptation ;  the  rays  also  appear 
colored  as  soon  as,  with  increasing  brightness,  they  become  visible  to 
the  fovea. 

The  results  of  Parinaud  have  been  disputed  by  Charpcntier,  and  they 
no  longer  harmonize  well  with  the  experiments  mentioned  on  page  244. 
According  to  Charpentier,  it  is  wrong  to  attribute  the  colorless  sensa- 
tion which  the  rays  of  very  feeble  brightness  call  forth  to  the  adaptation 
of  the  eye,  and,  on  the  other  hand,  it  is  certain  that  if,  from  full  daylight, 
we  enter  a  relatively  dark  space,  we  cannot  distinguish  right  away  colors 
which  we  observe  very  well  later. 

Nevertheless,  adaptation  plays  a  considerable  part  in  relation  to  these 
phenomena  as  the  following  observation  of  Charpentier  shows.  He 
covered  the  plate  B  of  his  photoptometer  (see  page  228)  with  a  black 
paper,  pierced  with  seven  small  openings  grouped  in  a  space  of  nine 
millimeters  square.  The  plate  A  was  illuminated  by  spectral  light  of 
different  colors.  On  opening  gradually  the  diaphragm  of  the  instru- 
ment, he  proved  that  the  first  impression  which  is  obtained  is  that  of  a 
diffuse  luminous  spot,  without  color;  let  us  designate  the  aperture  of 
the  diaphragm  for  the  moment  by  a.  To  distinguish  the  color  it  was 
necessary  to  give  the  diaphragm  a  larger  aperture  b,  and  it  is  only  by 
making  the  aperture  still  greater  c  that  we  come  to  distinguish  the 
points.  For  the  eye,  adapted  to  darkness,  the  apertures  b  and  c  remain 
almost  the  same  as  for  the  non-adapted  eye,  while  the  aperture  a  dimin- 
ishes enormously  especially  for  the  more  refrangible  colors. 

It  is  not  strange  that  there  exist  differences  of  opinion  on  these  ques- 
tions, for  there  is  very  little  certainty  in  the  determination  of  the  lower 
limits  of  the  sensations.  It  must  also  be  noted  that  the  expressions 
"adapted"  and  "non-adapted"  applied  to  the  eye  are  vague.  If  every  one 
is  in  accord  in  considering  an  eye  adapted  when  it  remains  for  half  an 
hour  in  darkness,  or  non-adapted  when  it  remains  as  long  in  full  day- 
light, the  authors  do  not  agree  so  well  in  designating  the  state  of  the 
eye  when  exposed  to  an  intermediary  illumination,  such  as  that  of  the 
interior  of  our  houses. 

107.  Methods  of  Mixing  Colors.  —  The  fundamental  examination  of 
the  color  sense  is  made  by  means  of  what  is  called  equations  of  colors: 
we  mix  two  or  three  colors  in  different  proportions  until  the  observer 
declares  the  mixture  similar  to  a  fourth  given  color,  most  frequently 
white.  We  then  examine  whether  an  eye,  of  which  the  color  sense  is 
normal,  recognizes  the  equation,  that  is  to  say,  whether  the  mixture 


248 


PHYSIOLOGIC   OPTICS 


appears  likewise  similar  to  white  for  this  eye.  —  We  can  mix  the  two 
colors  in  different  ways. 

i°  Mixtures  of  Spectral  Colors.  We  form  two  spectra  by  means  of 
two  prisms,  and  by  allowing  these  spectra  to  slide  over  one  another  we 
can  mix  any  two  hues  from  them.  Helmholtz  accomplished  the  same 
end  with  a  single  prism,  by  using  a  slit  in  the  form  of  V;  each  of  the 
branches  formed  an  oblique  spectrum,  and  the  two  spectra  would  over- 
lap to  a  great  extent  so  that  we  could  obtain  all  possible  mixtures. 

The  apparatus  of  Maxwell  was  very  ingenious.  It  consisted  of  a  box, 
a  section  of  which  is  shown  in  figure  157.  At  E  is  a  narrow  slit  through 
which  passes  light,  which  is  reflected  by  the  mirror  e  towards  the  prisms 


Fig.  157.  —  "  Color  box  "  of  Maxwell 


P  and  Px,  through  which  it  passes  to  meet  the  concave  mirror  S.  This 
mirror  reflects  the  light  which  passes  again  through  the  prisms  to  go  to 
form  a  spectrum  on  the  far  end  of  the  box,  AB.  At  this  place  are  three 
movable  slits  x,  y  and  z,  which  permit  spectral  light  of  any  hue  to  leave 
the  box  through  each  of  the  slits  by  displacing  them.  —  Suppose  x  cor- 
responds with  the  red,  y  with  the  green  and  z  with  the  violet.  It  must 
be  noted,  in  consequence  of  the  reversibility  of  optic  processes,  that  if 
we  illuminate  the  slit  x  from  the  outside  by  red  light,  this  light  will 
reach  an  eye  placed  at  E ;  but  if  we  illuminate  the  same  slit  with  green 
light,  this  light  will  not  reach  an  eye  at  E,  but  will  be  projected  to  one 
side  of  E.  In  order  that  the  green  light  reach  E,  it  must  pass  through 
the  slit  y.  Consequently,  illuminating  the  three  slits  x,  y  and  z  by  a 
white  luminous  source,  an  eye  placed  at  E  sees  the  surface  of  the  prism 
P  colored  by  the  mixture  of  the  three  colors,  which  a  flame  placed  at 
E  would  project  on  the  slits  x,  y  and  z.  —  At  the  far  end  of  the  box  is 
yet  another  aperture  c  through  which  enters  white  light,  which,  after 
having  been  reflected  by  the  mirror  M  and  concentrated  by  the  lens  L, 
meets  a  plate  of  ground  glass  blackened  on  the  back  Mx.  Xhe  eye  placed 
at  E  sees  this  plate  at  the  side  of  the  prism,  and  can  thus  compare  the 
brightness  and  color  of  the  mixture  with  that  of  the  white  light,  ad- 


THE  COLOR  SENSE  249 

mitted  through  c.  By  properly  placing  and  opening  the  slits,  we  can 
thus  obtain  a  mixture  which  is  not  distinguishable  from  the  white  light 
reflected  by  Mly  either  as  to  color  or  brightness. 

The  latest  researches  on  the  mixtures  of  colors  (Kcenig  and  his  pupils) 
have  been  made  with  a  large  spectral  instrument,  which  was  constructed 
for  the  laboratory  of  Berlin,  and  a  description  of  which  is  found  in  the 
second  edition  of  Helmholtz's  work  on  Physiologic  Optics  (page  355). 

2°  Max^vell  also  studied  the  mixtures  of  colors  by  placing,  on  the  disc 
of  Masson,  sectors  of  different  colors  (see  page  260). 

3°  We  can  mix  colors  by  means  of  a  plate  of  glass  ab  (fig.  158),  which 


Yellow  Blue 

Fig.   158.  —  Mixture  of  colors  by  means  of  a  glass  plate. 

is  held  so  that  it  may  reflect  rays  of  one  color  at  the  same  time  that  it 
allows  rays  of  another  color  to  pass  (Lambert). 

4°  Looking  at  two  colors  placed  side  by  side  through  a  double  refract- 
ing prism,  we  see  them  separated  by  a  strip  the  coloration  of  which  is 
that  of  the  mixture. 

5°  Placing  two  glasses  of  different  colors  before  the  two  openings  in 
the  experiment  of  Scheincr  and  looking  at  the  sky,  we  see  the  common 
part  of  the  circles  of  diffusion  in  the  color  of  the  mixture. 

6°  Painters  frequently  use  mixtures  of  coloring  matter,  but  the  results 
which  are  thus  obtained  are  frequently  not  in  accord  with  those  which 
are  obtained  by  the  other  methods.  The  best  known  example  is  the 
mixture  of  yellow  and  blue.  Painters  thus  obtain  green,  while  with  a 
revolving  disc  we  obtain  a  gray-white  (Lambert).  Hclmliolts  gave  the 
following  explanation  of  this  difference:  mixing  the  colors  of  yellow 
and  blue  pigment  the  superficial  molecules  send  back  yellow  light  and 
blue  light.  Together  these  rays  produce  the  impression  of  white,  as  on 
the  revolving  disc.  The  blue  molecules  situated  deeper  also  send  back 


250 


PHYSIOLOGIC  OPTICS 


blue  light,  but  it  must  be  noted  that  this  blue  light,  as  also  that  of  the 
superficial  molecules,  is  not  pure:  by  the  spectroscope  we  find  that  it 
contains  green,  blue  and  violet  rays.  The  yellow  molecules  send  back 
red,  yellow  and  green  rays.  Generally  the  molecules  allow  to  pass  rays 
of  the  same  color  as  those  which  they  send  back.  Among  the  rays  re- 
flected by  the  deep  yellow  molecules,  only  green  rays,  therefore,  can  pass 
through  the  superficial  blue  molecules,  and,  among  those  reflected  by 
the  deep  blue  molecules,  likewise  only  the  green  rays  can  pass  through 
the  superficial  yellow  molecules.  The  result,  therefore,  becomes  a  green 
color,  mixed  with  the  white  reflected  by  the  surface. 

108.  Results  of  the  Mixtures  of  Colors.  —  Newton  devised  his  table  to 
give  a  graphic  illustration  of  the  results  which  are  obtained  by  mixing 
colors.  The  principle  of  this  table  is  that  all  the  colors  we  can  produce 
by  mixing  two  given  colors  are  placed  on  the  straight  line  which  joins 
these  two  colors,  and  so  much  nearer  to  that  one  of  the  two  colors  which 


Green 


Yellowish-Green 


Bluish-Green 


Yellow 


Blue 


Indigo 


Red 

Purple 

Fig.  159.  —  Table  of  colors  after  Newton. 


enters  most  into  the  mixture.  The  quantity  of  the  color  of  the  mixture 
is  expressed  by  the  sum  of  the  quantities  of  the  component  colors.  Sup- 
pose, for  example,  that  we  want  the  result  of  the  mixture  of  three  parts 
of  green  with  one  part  of  red  and  two  parts  of  blue.  We  begin  by 


THE   COLOR  SENSE  251 

joining  the  green  and  red  by  a  straight  line  which  is  divided  into  two 
by  the  point  p  (fig.  159),  so  that  the  distance  of  p  from  the  green  may 
be  a  third  of  its  distance  from  the  red ;  p  is  then  the  place  of  the  mixture 
of  the  green  and  red,  the  mixture  being  represented  by  the  number  4, 
the  sum  of  the  two  component  colors.  We  then  join  the  point  p  with 
the  blue  by  a  second  straight  line  which  is  divided  into  two  by  the  point 
q,  so  tjiat  the  distance  pq  is  to  the  distance  of  q  from  the  blue,  in  the 
proportion  of  2  to  4 ;  q  is  the  place  of  the  mixture  of  the  three  colors,  and 
the  quantity  of  this  mixture  is  expressed  by  the  number  6.  Drawing 
the  line  oq  and  prolongating  it  until  it  cuts  the  spectral  curve,  we  see 
that  the  color  of  the  mixture  is  a  bluish-green  strongly  diluted  with 
white. 

There  enters  into  this  illustration  of  Newton  an  expression  which  is 
not  defined,  that  of  the  quantity  of  the  colors.  While  it  is  easy  to  tell 
what  must  be  expected  from  equal  quantities  of  the  same  color,  it  is  not 
easy  to  define  the  expression  of  equal  quantities  of  two  different  colors, 
the  result  of  which  is  that  the  form  of  the  curve  becomes,  up  to  a  certain 
point,  arbitrary.  With  Newton,  we  must  consider  as  equal  the  quantities 
of  two  complementary  colors,  which,  when  mixed,  give  white,  since  the 
white,  on  his  table,  is  situated  at  an  equal  distance  from  both.  If  we 
take  two  other  complementary  colors,  we  must  also  consider  as  equal 
the  quantities  of  these  colors  which,  mixed,  give  white,  but  on  condition 
that  this  white  be  of  the  same  brightness  as  the  former.  As  we  shall 
see,  Maxwell  and  Helmholtz  used  other  definitions. 

The  table  of  Newton  shows  that,  with  the  exception  of  purple,  we  can- 
not produce  new  colors  by  mixing  spectral  colors,  for  we  can  always, 
after  having  found  the  position  of  the  mixture,  draw  a  straight  line 
passing  through  the  center  and  this  point.  Prolonged,  this  straight 
line  will  meet  a  spectral  color,  and  the  mixture  is  equal  to  this  color 
diluted  with  white. 

The  table  of  Newton  indicates  also  another  peculiarity  of  the  normal 
color  sense,  namely  the  fact  that  we  can  reproduce  all  existing  hues 
by  mixing,  two  by  two,  three  colors  properly  chosen.  Let  us  select,  for 
example,  red,  green  and  blue,  and  draw  on  the  table  (fig.  159)  straight 
lines  which  join  these  colors.  If,  then,  we  select  any  spectral  color,  we 
can  always  join  it  to  the  center  of  the  table  by  a  straight  line;  this 
straight  line  must  necessarily  cut  one  of  the  sides  of  the  red-green-blue 
triangle  and  at  the  place  of  intersection  is  found  the  mixture  which  is 
similar,  in  hue,  to  the  spectral  color.  On  account  of  this  peculiarity  the 
normal  eye  is  called  trichromatic.  Observe  particularly  that  I  have  said 


252 


PHYSIOLOGIC   OPTICS 


that  the  two  colors  are  alike  as  to  hue.  Generally  they  are  not  alike  as 
to  purity,  the  color  of  the  mixture  being  diluted  with  white.  The  table 
of  Newton  also  requires  that  ,the  spectral  color  must  always  have  greater 
purity,  for,  if  we  could,  by  mixing  two  spectral  colors,  reproduce  a  third 
color  exactly,  these  three  colors  should  be  placed  on  a  straight  line,  and 
the  spectral  curve  could  not  be  circular.  But  this  last  condition  of  the 
table  is  not  fulfilled. 


Bluish-Green 


Yellow 


Orangi     6lV 


Fig.   160.  —  Color  table  of  Maxudl. 

The  accuracy  of  the  illustration  of  Newton  has,  indeed,  been  verified 
by  the  admirable  works  of  Maxwell.  This  author  found  that  Newton's 
table  gives  a  very  exact  illustration  of  the  results  of  the  mixtures  of 
colors,  but  that  the  spectral  colors  cannot  be  arranged  in  a  circle,  be- 
cause there  are  quite  extended  parts  on  the  spectrum,  the  colors  of 
which  can  be  reproduced  exactly,  or  nearly  exactly,  by  the  mixture  of 
two  given  colors,  and  which,  consequently,  must  be  placed  on  straight 
lines. 

Figure  160  shows  the  spectral  curve  of  Maxwell.  While  the  curve  of 
Newton  must  be  considered  merely  as  a  conception  of  the  mind,  Maxivcll 


THE  COLOR  SENSE 


253 


determined  his  experimentally  with  the  instrument  described  in  the  pre- 
ceding chapter  (fig.  161).  To  use  it  he  placed  it  in  such  a  position  that 
the  slits  .r,  y,  z  and  c  were  turned  towards  a  sheet  of  white  paper  illumi- 
nated by  the  sun.  As  a  starting  point  he  selected  the  three  following 
colors  (standard  colors) : 


Wave  length : 


Red  (R) 
0.630/i 


Green  (G) 
0.528  n 


Blue  (Bl) 
0.457  p 


He  placed  the  slits  x,  y  and  z  so  as  to  give  access  to  these  colors,  and, 
by  regulating  the  width  of  the  slits,  he  produced  a  mixture  which  differed 
neither  in  tint  nor  brightness  from  white  introduced  through  the  slit  c. 


Fig.  161.—"  Color  box  "  of  Maxwell. 

By  measuring  the  slits  he  found  for  x  a  width  of  2.36  mm.,  for  y  3.99 
mm.  and  for  z  3.87  mm.,  and  by  designating  the  white,  which  remained 
constant  through  all  the  experiments,  by  W,  he  had  thus  the  equation 

2.36  R  -f  3.99  G  +  3.87  Bl  =  W 

He  then  displaced  the  slit  x  so  as  to  give  access  to  orange  light ;  by 
regulating  the  slits  he  again  produced  a  mixture  similar  to  white  which 
gave  him  the  equation 

2.04  Or  -f-  3.25  G  -f  3.88  Bl  =  W 

As  white  was  the  same  in  both  cases,  we  can  combine  the  two  equa- 
tions, which  gives 


or 


or 


2.04  Or  -f  3.25  G  +  3.88  Bl  =  2.36  R  -f  3.99  G  +  3.87  Bl 
2.04  Or  =  2.36  R  4-  0.74  G  —  0.01  Bl 
1  Or  =  1.155  R  +  0.362  G  —  O.f  06  Bl 


He  then  repeated  the  measurement  for  the  other  colors,  by  always 
combining  two  of  the  standard  colors  with  the  color  in  question  to  pro- 
duce white.  He  thus  succeeded  in  expressing  all  the  colors  of  the  spec- 


254 


PHYSIOLOGIC   OPTICS 


trum  by  three  colors.    The  following  table  shows  the  results  of  these 
measurements : 


COLOR. 

&              "* 

BLUE 

p 

UNITY 

•p    j                                               .  

5.63     (663)  =        2.36    +    0.05    • 

h    0.36 

2.77 

2.032 

2.36     (630)  =        2.36    -f    0.00    • 

h   o.oo 

2.36 

1 

2.04     (606)  =        2.36    +    0.74    - 

-    0.01 

3.09 

0.662 

Yellow          .  .     .   .    ! 

2.79     (583)  =        2.36    +     2.45    - 
3  20     (562)  —        1  55     4-     3  99    - 

-    0.01 
-    0.10 

4.80 
5.43 

0.582 
0.589 

3  30     (544)  =        0.42     4-    3.99    • 

-    0.03 

4.38 

0.754 

f 

3.99     (528)  =        0.00     -\-    3.99 

f    0.00 

399 

I 

Green  ) 

i 

Blue  ! 

5.26     (513)  =  —  0.33     4-    3.99    - 
787     (500)  =  —  0.43     4-    3.99    - 
7.83     (488)  =  —  0.39     4-     2.67 
514     (477)  —  —  024     4-    0.98    - 

{-    0.44 
f     2.22 
f     3.87 
f    3  87 

4.10 
5.77 
6.15 
4.61 

.  282 
1.363 
1.275 
1.116 

4.28     (467)  =  —  0.14     4-     0.14    • 

f    3.87 

3.87 

1.105 

f 

3.87     (457)  =        0.00     4-     0.00    • 

f    3.87 

3.87 

1 

Violet  

4.10     (449)  =        0.08     4~     0.03     - 
5.59     (441)  =        014     +    0.09    - 
8.09     (434)  =        0.04     —    0.23    • 

3.87 
f     3.87 
f     3.87 

3  98 
4.10 
3.68 

J  A'oZ 

1.362 

2.197 

By  dividing  each  equation  by  the  coefficient  on  the  left,  we  obtain 
the  expression  corresponding  to  the  width  of  the  slit  of  I  millimeter. 


60          :»8  56          St-          52  50 

O»>  Y  G  Bl 

Fig.  162.  —  Color-curves  of  Maxwell. 


THE   COLOR  SENSE  255 

Under  this  form  the  result  is  found  expressed  on  figure  162.  The 
three  curves,  designated  by  R,  G,  B,  correspond  to  the  three  standard 
colors;  the  numbers  underneath  are  the  wave  lengths  of  the  different 
colors  of  the  spectrum,  and  the  position  of  the  three  points  in  which  the 
curves  cut  the  vertical  line  corresponding  to  each  of  the  colors,  indicates 
the  quantities  of  the  three  standard  colors  needed  to  produce  the  mixture. 

The  negative  sign  of  the  blue,  in  the  equation  of  the  orange,  is  found 
again  for  the  greater  number  of  the  colors  added  to  one  or  other  of  the 
standard  colors.  Its  significance  is  easy  to  grasp.  In  fact,  if  we  write 
the  equation  of  the  orange  thus : 

2.04  Or  +  0.01  Bl  =  2.36  K  +  0.74  G 

it  indicates  that  we  cannot,  with  the  three  standard  colors,  produce  a  mix- 
ture exactly  like  orange,  but  must,  on  the  contrary,  add  a  little  blue  to 
the  orange  so  that  it  may  be  like  the  mixture  of  red  and  green. 

It  should  be  noted  that,  up  to  the  present,  I  have  simply  expressed 
the  quantity  of  a  color  by  the  width  in  millimeters  of  the  slit  giving 
access  to  this  color.  To  construct  the  table  of  colors  we  do  the  same 
for  the  three  standard  colors;  but  for  other  colors  we  will  be  obliged  to 
select  the  units  in  another  manner.  I  have  said,  indeed,  that  with  Newton 
the  quantity  of  a  mixture  is  considered  as  equal  to  the  sum  of  the  quan- 
tities of  the  component  colors.  The  sum  of  the  three  component  colors 
of  the  orange  was 

2.36  +  0.74  —  0.01  =  3.09 

while  the  width  of  the  slit  was  2.04  mm.  According  to  Newton,  the 
quantity  of  orange  passing  through  the  slit  of  2.04  mm.  is,  therefore, 
3.09,  that  is  to  say,  the  unit  of  the  orange  corresponds  to  a  width  of  the 
slit  of  |;JJ  =  0.662  mm. 

If  we  wish  to  use  the  table  to  solve  questions  of  mixtures  of  colors 
we  must,  therefore,  multiply  the  quantities  found  by  the  table  by  the 
figures  indicating  the  units,  in  order  to  obtain  a  result  expressed  by 
the  width  of  the  slit  in  millimeters.  The  units  are  in  the  last  column 
of  the  table.  They  are  obtained  by  dividing  the  coefficients  on  the  left 
by  the  figures  in  the  column  before  the  last,  which  indicate  the  sum  of 
the  component  colors. 

To  construct  the  spectral  curve,  we  begin  by  drawing  the  dotted  equi- 
lateral triangle  of  figure  163.  We  suppose  the  three  standard  colors  placed 
at  the  three  angles,  an  arrangement  which  was  proposed  by  Young. 
To  find  the  position  of  the  orange,  we  begin  by  dividing  the  red-green 


256 


PHYSIOLOGIC   OPTICS 


side  into  two  parts,  in  the  proportion  of  0.74  :  2.36.  Let  P  be  the  point 
of  division:  join  this  point  to  the  blue  angle  by  a  straight  line,  of  which 
we  measure  the  length  a.  The  color  at  P  can  be  considered  either  as  a 
mixture  of  2.36  R  with  0.74  G,  or  as  a  mixture  of  3.09  Or  with  o.oi  Bl. 
It  follows  that  the  orange  must  be  placed  on  the  prolongation  of  a, 
beyond  the  point  P,  and  by  designating  its  distance  from  P  by  x  we 
should  have  x  =JS  a-  This  distance  is,  for  the  orange,  so  small  that  it 


Green 


50       Bluish-Green 


Yellow       // 
ft 


Fig.  163.  —  Color  table  of  Maxwell. 


is  scarcely  visible  on  the  figure,  the  curve  coinciding  at  this  position 
almost  with  the  dotted  line.  —  We  observe  that,  on  account  of  the  pres- 
ence of  the  negative  coefficient,  the  color  in  question  must  be  placed 
outside  of  the  triangle.  A  color  which  is  situated  in  the  interior  of  the 
triangle  may  be  reproduced  exactly  by  a  mixture  of  the  three  standard 
colors;  this  is  not  possible  for  a  color  situated  outside  of  the  triangle: 


THE  COLOR  SENSE  257 

it  is  necessary,  on  the  contrary,  to  mix  it  with  one  of  the  standard  colors, 
in  order  that  it  may  seem  equal  to  the  mixture  of  the  two  others. 

On  the  table  of  Maxwell  the  greater  part  of  the  spectrum  (from  0.63  M 
in  the  orange-red  to  0.53  /*  in  the  green,  and  from  0.5 I/A  in  the  green  to 
0.47  ,a  in  the  blue)  is  arranged  on  the  two  sides  of  a  triangle  of  which 
the  green,  between  0.53  v  and  0.51  /*,  forms  a  rounded  angle,  while  the 
extremities  of  the  spectrum  form  two  other  somewhat  irregular  angles. 
We  must  imagine  the  third  side  of  the  triangle  occupied  by  the  purple 
colors,  which  are  obtained  by  mixing  red  with  blue.  As  nearly  all  the 
spectral  colors  have  one  of  the  coefficients  negative,  almost  the  entire 
curve  is  situated  outside  of  the  triangle  of  the  standard  colors,  which  in- 
dicates that  the  mixture  colors  have  nearly  all  a  little  less  purity  than 
the  spectral  colors.  The  part  situated  between  the  red  and  the  green 
coincides,  however,  very  nearly  with  the  corresponding  side.  By  select- 
ing another  standard  color,  green,  we  could  make  the  part  of  the  curve 
situated  between  0.51  ^  and  0.47  P  coincide  with  the  other  side  of  the 
triangle,  but  it  is  easy  to  see  that  we  cannot  select  the  green  color  so 
as  to  make  the  two  sides  coincide  with  the  curve  at  once.  We  cannot, 
therefore,  select  three  spectral  colors  such  that  we  can  reproduce  all  the  other 
spectral  colors  exactly  by  their  mixtures;  we  can  reproduce  all  the  hues,  but 
some  of  >  the  mixture  colors  always  continue  to  have  less  purity  than 
the  corresponding  spectral  colors,  whatever  may  be  the  standard  colors 
we  have  chosen. 

By  means  of  the  table  of  Maxwell  we  can  construct  the  result  of  ^nix- 
tures  of  any  colors.  If  we  mix  two  colors  placed  on  the  same  side  of 
the  approximately  triangular  curve,  we  obtain  a  mixture  color  which 
has  as  much  purity  as  the  spectral  color,  while  if  we  mix  two  colors 
situated  each  on  a  different  side,  we  obtain  a  mixture  strongly  diluted 
with  white.  The  three  colors  which  Maxwell  selected  as  standard  colors, 
the  red,  green  and  blue,  have,  therefore,  this  peculiarity  that  they  cannot 
be  reproduced  by  mixing  other  spectral  colors,  the  mixture  being  always 
strongly  diluted  with  white.  —  The  approximately  triangular  form  of 
the  curve,  with  the  three  colors,  red,  green  and  blue,  placed  at  the  angles, 
does  not  depend  on  the  choice  of  the  standard  colors.  By  means  of  the 
equations  of  Maxwell,  we  can,  by  a  simple  calculation,  express  all  the 
spectral  colors  by  three  colors  other  than  his  standard  colors,  for  example 
by  orange,  blue-green  and  blue.  The  curve  even  then  retains  its  approx- 
imately triangular  form,  having  the  red,  green  and  blue  at  the  angles, 
but  it  differs  considerably  from  the  equilateral  triangle  formed  by  the 
straight  lines  joining  the  three  new  standard  colors,  which  indicates  that 


258  PHYSIOLOGIC   OPTICS 

the  mixture  colors  have,  in  this  case,  very  little  purity.  Maxwell  selected 
red,  green  and  blue,  so  that  the  curve  would  come  as  near  the  triangle 
in  form  as  possible. 

Contrary  to  what  has  taken  place  in  the  case  of  these  three  colors, 
those  which  are  placed  on  each  of  the  two  sides  of  the  triangular  curve, 
may  be  reproduced  exactly  by  mixing  other  spectral  colors.  They  are, 
in  this  regard,  analogous  to  the  purple  colors  which  are  obtained  by 
mixing  the  red  and  spectral  blue,  and  which  appear  to  the  eye  as  pure 
as  the  pure  spectral  colors. 

The  most  interesting  phenomenon  among  the  great  number  of  facts 
which  are  expressed  by  the  table  of  Maxwell,  is  certainly  this,  that  we 
can  produce  a  perfect  sensation  of  yellow  by  mixing  red  and  green. 
The  fact  was  already  known  to  Young,  and  formed  the  principal  basis  of 
his  theory  of  colors,  which  I  shall  mention  later  on.  Lord  Raleigh  had 
constructed  a  special  instrument  for  determining  the  quantities  of  spec- 
tral red  and  spectral  green  necessary  to  produce  a  complete  equality 
with  spectral  yellow.  In  his  numerous  examinations  he  could  always 
obtain  a  perfect  equality,  but  in  the  matter  of  the  quantities  required  of 
the  component  colors,  he  found  quite  unexpected  individual  differences 
(see  page  262).  We  can  also  mix  the  light  of  the  lithium  and  thallium 
flames  so  as  to  obtain  a  light  which  cannot  be  distinguished  from  that 
of  the  sodium  flame.  Another  method,  also  pointed  out  by  Lord  Raleigh, 
consists  in  looking  through  a  liquid  which  allows  only  red  and  green 
rays  to  pass  (a  mixture  of  bichromate  of  potash  and  blue  aniline  dis- 
solved in  water).  By  observing  through  this  liquid  an  object  of  a  bright 
white,  a  cloud  illuminated  by  the  sun  for  example,  it  appears  of  a  pure 
yellow,  although  all  the  yellow  rays  are  completely  absorbed.  —  The 
liquid  is,  besides,  very  sensitive  to  tints  of  white  light ;  the  light  of  the 
blue  sky,  which  contains  too  little  red,  appears  greenish,  while  the  light 
of  an  arc  lamp  appears  reddish. 

The  yellow  occupies  a  special  position  among  the  colors.  An 
observer  completely  ignorant  of  the  results  of  the  mixtures,  as  well 
those  of  the  physicists  who  obtain  yellow  by  mixing  spectral  red  and 
green,  as  those  of  the  painters  who,  with  their  pigments,  obtain  green 
by  mixing  yellow  with  blue,  would  probably  be  tempted  to  class  the 
yellow  among  the  three  standard  colors  of  Maxwell,  so  as  to  reckon  four 
principal  colors  in  the  spectrum:  red,  yellow,  green  and  blue.  As  we 
have  seen,  the  yellow  is  distinguished  from  the  three  others  in  that  it 
can  be  reproduced  by  a  mixture  of  other  colors.  In  this  respect  it  is 
analogous  to  the  colors  which  are  placed  on  the  other  sides  of  the 


THE  COLOR  SENSE  259 

triangle,  the  purple  and  the  blue-green,  and  it  is  distinguished  from  the 
latter  in  this  that  the  eye  may  not  perceive  any  trace  of  red  or  green  in 
the  yellow,  while  no  one  would  hesitate  to  declare  that  he  saw  blue  and 
red  in  the  purple,  or  green  and  blue  in  the  blue-green.  The  yellow,  in 
this  regard,  resembles  white  in  which  the  eye  no  longer  distinguishes 
any  trace  of  the  component  colors.  The  yellow  is  also  that  one  of  the 
spectral  colors,  which,  to  the  eye,  seems  to  offer  most  resemblance  to 
white.  —  Another  peculiarity  of  the  yellow,  on  which  Herschel  laid 
stress,  is  the  considerable  change  which  this  color  undergoes  when  its 
brightness  diminishes.  A  dark  blue  still  seems  blue,  while  a  dark  yellow 
appears  brown,  a  color  which  the  observer  not  prejudiced  would  con- 
sider rather  as  a  special  color. 

We  can  obtain  the  impression  of  white  in  many  different  ways.  The 
celebrated  experiment  by  which  Newton  combined  by  means  of  a  lens  all 
the  colored  rays  of  the  spectrum  in  a  white  image  shows,  in  the  first  place, 
that  all  the  colors  of  the  spectrum,  when  mixed,  give  white.  The  equa- 
tions of  Maxwell  furnish  a  long  series  of  examples  of  the  possibility  of 
forming  white  by  mixing  three  colors.  Lastly  the  table  indicates  a  great 
number  of  pairs  of  complementary  colors,  that  is  to  say,  colors  which, 
mixed  two  by  two  in  the  proper  proportions,  give  white.  To  find  the 
color  complementary  to  a  given  color,  we  have  only  to  prolong  the  line 
which  joins  it  to  the  white,  until  it  meets  the  curve  again.  The  point  of 
intersection  is  the  place  of  the  complementary  color,  and  the  quantities 
to  take  of  both  colors  are  inversely  proportional  to  their  distances  from 
the  white.  We  must  recollect,  however,  that  if  we  wish  to  express  the 
quantity  by  the  width  of  the  slit  in  millimeters,  we  must  reduce  the 
numbers,  as  already  pointed  out. 

A  glance  at  the  table  shows  that  the  green  colors  (greenish)  from 
57  to  49.5  have  no  complementary  colors  in  the  spectrum.  Their  com- 
plementaries  are  the  purple  colors.  The  complementaries  of  the  red 
extremity,  up  to  61,  are  situated  very  near  one  another  (from  49.5  to 
49.2),  those  of  the  blue  extremity  are  condensed  near  57.  The  hue 
varies,  therefore,  very  slowly  towards  the  extremities  of  the  spectrum, 
while  the  variation  reaches  its  greatest  rapidity  in  the  blue-green,  where 
the  divisions  are  separated  by  very  marked  intervals. 

Maxwell  did  not  determine  the  extreme  parts  of  the  spectrum;  one 
might  think,  therefore,  that  the  curve  ought  to  be  really  more  extended ; 
but,  according  to  the  researches  of  Koenig  and  Dieterici,  this  is  not  the 
case.  These  authors  made  a  long  series  of  very  minute  researches,  like 
those  of  Maxwell,  with  their  large  spectral  instrument.  Their  results 


260  PHYSIOLOGIC  OPTICS 

seemed  to  agree  well  with  those  of  the  latter  author;  however,  they 
could  not  verify  the  bend  which  the  curve  of  Maxwell  makes  in  the  red. 
According  to  these  authors,  the  hue  does  not  vary  in  the  spectrum 
beyond  67  and  43,  so  that  the  divisions  beyond  these  limits  must  on  the 
table  coincide  with  these  limits.  Maxwell,  indeed,  himself  calls  the  form 
of  the  extremities  of  the  curve  somewhat  doubtful. 

If  we  compare  the  complementary  quantities  of  red  and  blue-green, 
we  notice  that  the  red  appears  darker  than  the  green.  To  illustrate 
facts  of  this  kind  on  the  table,  Helmholtz  supposed  as  equal  quantities 
of  two  different  colors  quantities  appearing  to  have  the  same  brilliancy. 
He  thus  obtained  the  spectral  curve  illustrated  in  figure  164.  The  small 
circle  indicates  the  position  of  the  white.  Since  the  red  complementary 


Yellow 


Violet 

Purple 
Fig.  164.  —  Color  table  of  Helmholtz. 

to  the  blue-green  appears  darker  than  the  latter,  we  consider  its  quantity 
as  smaller  and  place  it  consequently  farther  from  the  white.  Indeed, 
such  a  comparison  of  the  brightness  of  two  different  colors  is  not  easy, 
as  Helmholtz  himself  remarked,  and  the  result  depends  besides  on  the 
phenomenon  of  Purkinje.  If,  for  example,  a  certain  quantity  A  of  yellow 
light  appears  to  have  the  same  brightness  as  the  quantity  B  of  blue  light, 
we  find  that  the  quantity  ~  of  yellow  light  will  appear  darker  than  the 
quantity  -|-  of  blue  light.  The  form  of  the  curve  would  vary,  therefore, 
according  to  the  brightness  used. 

Maxwell  showed  how,  without  the  help  of  a  spectral  instrument,  we 
can  make  determinations  analogous  to  his  own  by  means  of  the  revolv- 
ing disc  of  Masson.  It  is  necessary  to  have  paper  discs  (colored,  whites 
and  blacks)  of  two  different  sizes,  so  as  to  be  able  to  make  two  mixtures 
at  once,  by  covering  the  central  part  of  the  large  disc  with  the  small 
ones. 

We  cut  the  discs  along  a  radius,  in  order  to  be  able  to  combine  them 
so  as  to  obtain  colored  sectors  of  any  angle.  We  select  three  standard 
colors,  the  red,  green  and  blue,  and  we  combine  three  large  discs  so  as 
to  have  a  sector  of  each  color.  In  the  middle  we  place  two  small  discs 
combined  so  as  to  have  a  black  and  a  white  sector.  Making  the  whole 


THE  COLOR  SENSE  261 

rotate,  we  obtain  in  the  middle  a  gray  circle,  surrounded  with  a  ring 
tinted  with  the  mixture  of  three  standard  colors.  By  regulating  the 
angles  of  the  sectors  we  make  the  two  tints  alike,  and  write  the  equation 
as  thus : 

165  R  -f  122  G  +  73  Bl  =  100  W  -f  260  B  (Aubert) 

W  denotes  the  white,  B  the  black,  and  the  numbers  indicate  the  angles 
of  the  sectors.  Neglecting  the  little  light  reflected  by  the  black,  we 
may  write : 

165  R  4-  122  G  +  73  Bl  =  100  W 

To  express  any  other  color,  the  yellow  for  example,  by  the  standard 
colors  we  replace  the  red  sector  by  a  sector  of  this  color.  Regulating 
the  size  of  the  sectors,  we  find  for  example : 

146  Y  +  17  G  4-  197  Bl  =  159  W  +  201  B 
or,  by  dividing  by  1.59, 

92  Y  +  11  G  4-  124  Bl  =  100  W 

We  then  combine  this  equation  with  that  of  the  standard  colors^  which 
gives 

92  Y  +  11  G  +  124  Bl  =  165  R  4-  122  G  +  73  Bl 
or 

1  Y  =  1.97  R  4-  1.21  G  —  0.55  Bl 

With  these  equations  we  can  construct  graphic  illustrations  of  the 
same  kind  as  figures  160  and  162,  and,  by  always  working  with  the  same 
kind  of  papers,  we  may  thus  study  and  compare  the  color  sense  of  differ- 
ent eyes;  but  the  spectral  method  always  remains  superior. 

109.  Abnormal  Trichromasia.  —  If  we  examine  a  certain  number  of 
persons  by  the  method  of  Maxwell,  on  constructing  the  color  table  of 
each  person,  we  often  find  small  differences :  a  mixture  which  one  ob- 
server declares  like  white,  seems  to  another  colored.  It  is  probable  that 
these  differences  are  due,  at  least  in  part,  to  the  fact  that  a  portion  of  the 
rays  is  absorbed  by  the  media  of  the  eye,  and  that  this  absorption  is 
more  pronounced  in  some  persons  than  in  others.  Thus  the  yellowish 
color  of  the  crystalline  lens  of  old  persons  indicates  that  it  must  absorb 
a  part  of  the  blue  rays.  A  mixture  of  yellow  and  blue,  which,  to  a 
normal  person,  appears  equal  to  the  white,  must  appear  yellowish  to  the 
old  person,  whose  crystalline  lens  absorbs  relatively  more  of  the  light 
of  the  mixture  than  of  the  white  light.  After  extraction  of  a  cataract, 
the  patient  often,  at  the  first  moment,  affects  to  see  all  blue,  almost  as 


U62  PHYSIOLOGIC   OPTICS 

everything  appears  tinted  with  the  complementary  color  when  we  have 
looked  for  a  little  while  through  a  colored  glass  and  then  remove  it 
suddenly.  Maxwell  attributed  some  of  the  phenomena  in  question  to 
the  absorption  of  the  green-blue  rays  by  the  yellow  pigment  of  the 
macula.  Looking  at  a  bright  line  through  a  prism,  he  observed  a  dark 
spot  corresponding  to  the  fovea,  which  moved  up  and  down  with  the 
look,  as  long  as  the  latter  remained  in  the  blue  part  of  the  spectrum, 
but  which  disappeared  as  soon  as  the  look  left  the  blue.  He  recom- 
mended also,  in  order  to  observe  the  phenomenon,  fixing  a  yellow  paper 
for  a  little  while,  and  then  transferring  the  look  to  a  blue  paper.  The 
spot  then  appears  for  some  moments.  Taking  two  equal  whites,  one 
made  of  ordinary  white  light  and  the  other  of  a  mixture  composed  in 
great  part  of  green-blue  rays,  the  latter,  seen  in  indirect  vision,  seemed 
greenish  and  more  luminous  than  the  former. 

We  have  seen  (page  198)  that  the  existence  of  the  yellow  pigment  of 
the  macula  may  appear  doubtful,  but  the  fact  that  the  macula  is  less 
sensitive  to  blue  than  the  remainder  of  the  retina  is  unquestionable.  I 
do  not  see  the  scotoma  in  the  blue  part  of  the  spectrum,  but  another 
observation  which  I  have  made  is  equally  convincing.  There  exist  in 
commerce  transparent  sheets  of  colored  gelatine  which  may  often  with 
advantage  replace  the  colored  glasses  in  many  experiments.  I  have 
such  a  sheet,  tinted  probably  with  an  aniline  color,  which  allows  the 
red  and  blue  rays  to  pass.  When,  looking  at  the  sky,  I  put  this  sheet 
before  my  eye,  I  see  at  the  point  fixed  a  somewhat  diffuse  red  spot, 
almost  the  size  of  the  moon  or  a  little  larger.  After  an  instant  it  dis- 
appears; if  then  I  remove  the  sheet  without  changing  the  direction  of 
the  look,  I  see  the  after-image  of  the  spot,  very  slightly  greenish 
and  clearer  than  the  surrounding  parts.  —  The  color  table  of  Maxwell 
himself  differs  somewhat  from  that  of  Mrs.  Maxwell,  illustrated  in  figure 
160,  differences  which  could  very  well  be  due  to  the  fact  that  inferiority 
of  the  macula  for  the  blue  was  more  pronounced  in  him  than  in  her. 

Neglecting  these  slight  differences,  an  equation  of  color  which  is  true  for 
a  normal  eye,  remains  true  for  all  eyes  as  weU  for  normal  €yes  as  for 
dichromatic  eyes. 

This  latter  assertion  was  considered  entirely  general,  until  Lord 
Rayleigh,  in  1880,  discovered  a  class  of  eyes  for  which  it  is  not  true. 
After  having  produced  a  mixture  of  spectral  red  and  spectral  green 
which  appeared  to  him  identical  with  spectral  yellow,  he  asked  a  certain 
number  of  people  to  compare  the  two  hues.  Most  of  them  found  the 
hues  identical,  but  some,  amongst  whom  were  his  three  brothers-in-law, 


THE   COLOR  SENSE  263 

declared  that  they  saw  scarcely  any  resemblance ;  the  pure  color  ap- 
peared yellow  to  them,  while  the  compound  color  seemed  to  them  nearly 
as  red  as  sealing  wax.  To  see  the  hues  alike,  these  persons  had  to  add 
so  much  green  to  the  mixture  that  it  appeared  nearly  pure  green  to  a 
normal  eye.  The  mixture  of  Lord  Rayleigh  was  3.13  R  +  i.oo  G;  that  of 
his  brother-in-law  1.5  R  +  i.o  G.  (i) 

The  persons  in  question  presented  no  other  anomalies  of  the  chro- 
matic system ;  they  were  by  no  means  dichromatics  (daltonists).  Later  re- 
searches (Bonders,  Kcenig  and  Dieterici)  confirmed  the  opinion  of  Lord 
Rayleigh  that  these  people  formed  a  group  by  themselves:  no  inter- 
mediary forms  have  been  found  between  their  anomaly,  which  Kcenig 
called  abnormal  trichromasia,  and  the  normal  chromatic  system.  The 
anomaly  seems  almost  as  frequent  as  dichromatism ;  Kcenig  and  Dieterici 
found  three  cases  of  it  among  seventy  persons  examined,  but  no  case  is 
known  in  which  the  anomaly  was  discovered  by  the  person  himself  who 
was  affected. 

110.  Color-Blindness  or  Dichromasia  (Daltonism).  —  The  most  preva- 
lent form  of  dyschromatopsia  is  called  daltonism  after  the  celebrated 
English  chemist,  Dalton,  who  was  affected  with  it,  and  who  gave  the  first 
fairly  exact  description  of  it.  It  is  calculated  that  about  4  per  cent,  of 
men  are  affected  with  this  anomaly ;  it  is  much  rarer  in  women,  especially 
in  its  complete  form. 

For  the  daltonists,  there  is  in  the  spectrum  a  place,  in  the  green-blue, 
the  color  of  which  resembles  white  (gray).  We  call  this  place  the  neutral 
point.  Instead  of  the  great  variation  which  the  normal  eye  perceives  in 
the  spectrum,  the  daltonists  see  only  two  colors:  one  which  they  most 
frequently  call  yellow,  and  which  fills  the  entire  part  situated  between 
the  neutral  point  and  the  red  extremity,  and  the  other  which  they  call 
blue,  and  which  extends  from  the  neutral  point  to  the  violet  extremity. 
In  no  part  belonging  to  either  of  the  colors  does  the  hue  change ;  there 
are  differences  of  purity  and  brightness  only.  The  color  called  yellow 
seems  to  them  pure  in  the  red,  orange,  yellow  and  green,  until  about 
0.54  P.  or  0.53  \L  near  the  line  E.  In  all  this  part  there  are  differences  of 
brightness  only ;  we  can  make  one  of  these  colors  like  any  other  color  by 
changing  the  brightness.  The  red  and  orange  of  the  spectrum  are  often 
so  feeble  that  they  are  not  perceived  unless  the  spectrum  is  very  clear. 
Starting  from  the  line  E,  the  color  becomes  more  and  more  grayish,  and 


(1)  The  numbers  are  not  comparable  with  those  of  Maxwell,  Lord  Rayleigh  having  probably  used 
colors  different  from  the  standard  colors.  Otherwise  Maxwell  and  Mrs.  Maxwell  would  both  have  be- 
longed to  the  category  of  abnormal  trichromasia,  which  is  not  at  all  probable. 


264  PHYSIOLOGIC   OPTICS 

at  the  neutral  point  in  the  neighborhood  of  0.50 />-  (see  fig.  165)  the  color 
is  like  gray.  The  brightness  diminishes  at  the  same  time ;  generally,  the 
daltonists  tell  you  that  the  parts  situated  near  the  neutral  point  are 
darker  than  those  situated  at  some  distance  away  from  it.  It  is  possible 
that  this  diminution  of  brightness  is  due  to  the  fact  that  the  neutral  point 
is  situated  in  the  green-blue  part  of  the  spectrum,  the  rays  of  which  are 
most  affected  by  the  influence  of  absorption  in  the  yellow  pigment  of 
the  macula,  a  phenomenon  which  often  seems  very  pronounced  in  the 
dichromatics.  Starting  from  the  neutral  point  the  other  color  called  blue 
begins  to  make  itself  felt:  gaining  in  purity,  it  becomes  pure  at  about 
0.46  /*,  and,  starting  from  this  point,  presents  differences  of  brightness 
only ;  the  maximum  is  near  the  place  where  the  color  becomes  pure. 

The  dichromatics  see,  therefore,  in  the  spectrum  only  two  colors,  but 
it  is  difficult  to  tell  which.  If  we  designate  the  colors  as  yellow  and  blue, 
it  is  not  a  sure  sign  that  the  spectral  colors  give  them  the  same  impres- 
sions as  those  which  we  obtain  by  yellow  and  blue.  Generally  speaking, 
it  is  impossible  to  communicate  to  any  one  the  nature  of  a  sensation 
which  we  experience  otherwise  than  by  a  comparison.  If,  for  example, 
one  man  told  another  that  an  object  had  a  sugary  taste,  he  only  means 
to  convey  that  the  object  gives  him  a  sensation  similar  to  that  which 
sugar  would  give  him.  The  other  can  then  verify  this  if  he  also  finds 
that  the  taste  of  the  object  is  similar  to  that  of  sugar,  and  if  he  finds  it 
so  he  will  say  that  the  former  has  a  normal  taste;  but  it  is  impossible 
to  tell  whether  the  object  has  the  same  taste  for  both.  —  As  we  cannot 
know  how  the  daltonists  see  colors,  Donders  proposed  to  replace  in  their 
case  the  expressions  of  yellow  and  blue  colors  by  those  of  warm  and  cold 
colors,  terms  which  are  in  use  among  painters. 

We  must  observe,  however,  that  while  in  all  other  known  cases  the 
daltonism  was  bilateral,  there  exists  in  literature  a  unique  case  of  uni- 
ocular  daltonism ;  it  is  clear  that  such  a  patient  would  be  well  qualified 
to  give  information  on  the  question  of  knowing  how  the  daltonists  see 
the  colors.  The  case  was  very  well  investigated  by  Hippel.  The  left  eye 
was  normal,  while  the  right  eye,  which  squinted,  but  which  had  been 
operated  on  and  presented  no  ophthalmoscopic  lesion,  showed  an 
anomaly  wholly  analogous  to  ordinary  daltonism.  The  neutral  point 
(situated  at  0.512  /*)  divided  the  spectrum  into  a  yellow  part  and  a  blue 
part.  The  red  and  green  of  the  spectrum  were,  in  hue,  similar  to  the 
yellow,  but  appeared  a  little  less  bright.  Now,  looking  at  the  yellow 
sodium  line,  first  with  one  eye  and  then  with  the  other,  the  subject  de- 
clared that  the  appearance  was  the  same  for  both  eyes,  apart  from  a 


THE  COLOR  SENSE 


265 


slight  diminution  of  brightness  for  the  dichromic  eye.  It  was  the  same 
for  the  blue  indium  ray  as  for  the  white.  If,  therefore,  we  can  consider 
the  case  of  Hippel  as  a  case  of  true  daltonism  the  difficulty  seems  solved. 
The  sensations  which  the  daltonists  designate  as  yellow  and  blue  would 
be  identical  with  those  of  normal  persons. 

As  color-blind  persons  recognize  the  equation  of  the  normal  eyes,  the 
colors  which  are  complementary  for  normal  eyes  are  also  complementary 
for  them.  It  follows  that  the  color  complementary  to  the  neutral  point 


Green 


Bluish-Green 


Yellow 


Fig.  165.  —  Color  table  of  Maxwell 


must  also  appear  gray  to  them  (or  be  invisible),  as  well  as  all  the  colors 
situated  on  the  diameter  of  the  table  which  joins  them.  As  the  colors 
next  to  the  neutral  point  appear  strongly  mixed  with  white,  their  com- 
plementaries,  as  long  as  they  are  in  the  spectrum,  must  appear  of  very 
little  brightness,  since  they  must  neutralize  only  the  little  chromatic 
value  which  is  in  these  grayish  colors. 


26G  PHYSIOLOGIC   OPTICS 

While  an  equation  of  colors,  which  is  true  for  a  normal  eye,  is  so  also 
for  the  color-blind,  the  reverse  is  not  true :  color-blind  persons  recognize 
as  similar,  mixtures  which  are  by  no  means  so  for  a  normal  eye.  For  a 
daltonist,  we  can  reproduce  the  impression  of  any  color  of  the  spectrum, 
as  well  as  that  of  white,  by  mixtures  of  two  colors.  On  account  of  this 
peculiarity,  the  anomaly  in  question  is  also  termed  dichromasia. 

Maxwell  used  two  of  his  standard  colors,  green  and  blue.  He  thus 
found,  for  a  dichromatic  student,  the  equation 

4.28  G  +  4.20  Bl  =  W. 

The  position  of  this  mixture  color  is  marked  on  the  table  (fig.  165)  by 
the  letter  k;  the  letter  K  indicates  the  corresponding  spectral  color, 
which  is  the  neutral  point.  As  the  daltonists  recognize  the  equations  of 
the  normal  eyes,  we  can  combine  this  equation  with  that  of  the  normal 
eye  (page  253) 

2.36  R  +  3.99  G  +  3.87  Bl  =  W. 

We  have,  therefore,  for  the  daltonist 

2.36  K  +  3.99  G  -f  3.87  Bl  =  4.28  G  -f  4.20  Bl, 
an  equation  which  we  can  also  write 

L  =  2.36  K  —  0.29  G  —  0.33  Bl  =  0. 

This  latter  color  would  not,  therefore,  produce  any  impression  on 
the  dichromatic  eye  and  would  represent,  up  to  a  certain  point,  the 
element  which  is  wanting  in  it.  Its  place  is  marked  by  the  letter  L  on 
the  table  (fig.  165).  As  L  is  situated  outside  the  spectral  curve,  it  is  a 
fictitious  color  which  really  does  not  exist,  but  which  we  must  suppose 
still  purer  than  the  corresponding  spectral  color  which  is  marked  /,  since 
it  is  situated  farther  from  the  white  than  the  latter.  Compared  with  L, 
/  is  to  be  considered  as  a  mixture  of  white.  Nor  is  it  wholly  invisible, 
but  very  feeble. 

For  his  daltonist,  Maxwell  succeeded  in  reproducing  all  the  colors  of 
the  spectrum  by  mixtures  of  his  two  standard  colors.  The  results  are 
represented  by  the  curves  in  figure  166.  Moreover,  it  would  be  simpler 
to  select  two  colors  which  appear  pure  to  the  daltonists,  as  van  der  Weyde 
and  latterly  Kcenig  and  Dieterici  have  done.  The  green  color  of  Maxwell 
seemed  to  the  daltonists  slightly  mixed  with  gray,  as  the  curves  show. 

On  the  table  of  colors  the  whole  chromatic  system  of  the  daltonists 
is  reduced  to  a  straight  line  (fig.  167),  since  all  the  colors  which  we  can 
produce  by  mixing  two  given  colors  must  be  placed  on  the  straight  line 


THE  COLOR  SENSE 


267 


which  joins  them.  The  line,  too,  corresponds  only  to  the  part  of  the 
spectrum  in  which  the  colors  are  seen  mixed  with  white,  because  all  the 
parts  where  the  colors  seem  pure,  must  come  together  in  the  two  points 
which  form  the  extremities  of  the  line. 

Examining  a  series  of  daltonists,  we  observe  that  the  position  of  the 
neutral  point  is  not  exactly  the  same  in  all.  It  varies  in  different  persons 
between  0.492^  and  0.502  //.  In  figure  165  these  two  points  are  marked 


0,8 


62  60     .     68  56  5*  St          -Sfl          %8          *«          ** 

^ A— V 

Or.  Y  G  Bl  I 

Fig.  166.  —Color  curves  of  a  dichromatic,  after  Maxwell. 

R  and  S ;  it  is,  therefore,  between  R  and  S  that  the  position  of  the  neutral 
point  may  vary,  and  consequently,  the  direction  of  the  neutral  diameter 
would  vary  between  RT  and  SQ.  There  results  a  certain  difference 
between  daltonists  whose  neutral  point  is  situated  nearer  R,  and  those 
in  whom  it  is  situated  nearer  S.  In  the  former,  the  neutral  diameter 
passes  through  the  green-blue  and  the  red  (i),  and  the  spectrum  seems 
shortened,  because  the  red  extremity  contains  the  colors  complementary 


(338 


51 


Fig.  167. — Color  table  of  a  dichromatic,  after  the  measurements  of  Koenig  and  Dieterici. 

to  the  grayish  colors  and  must,  consequently,  as  we  have  seen,  appear 
very  dark.  In  the  others,  the  neutral  point  corresponds  to  a  color  situ- 
ated nearer  the  green,  the  complementary  of  which  is  purple,  and  not 

(1)  In  order  not  to  depart  from  the  terminology  which  is  generally  used,  I  hare  designated  the 
colors  from  0.62  to  0.63  ^  as  reds,  but  it  must  be  noted  that  with  the  division  of  the  spectrum  which  I 
have  adopted  in  figure  151,  and  which  was  proposed  by  Listing,  these  colors  are  already  in  the  orange. 
On  the  other  hand,  Chibret  found  with  his  instrument  that  the  colon  which  the  daltonists  confound 
most  frequently  are  the  orange  and  blue. 


268  PHYSIOLOGIC  OPTICS 

found  in  the  spectrum.  As  the  colors  complementary  to  the  gray  parts 
of  the  spectrum  do  not  correspond  to  the  red  extremity,  the  latter  pre- 
serves its  ordinary  intensity  and  the  spectrum  is  not  seen  shortened. 

Guided  especially  by  theoretical  considerations  (see  page  273),  it  has 
been  proposed  to  distinguish  between  these  two  forms  by  designating  the 
former  as  anerythropsia  (Rothblindheit),  the  latter  as  achloropsia  (Griin- 
blindheit).  It  was  Seebeck  who  first  distinguished  between  these  two 
forms ;  but  although  he  has  been  followed  by  a  great  number  of  scientists, 
among  others  by  Hclmholtz,  Holmgren,  Leber  and  Kccnig,  this  distinction 
does  not  yet  seem  completely  justified.  If  the  neutral  diameter  had 
always  either  the  direction  SQ  or  the  direction  RT,  it  would  be  reason- 
able to  distinguish  between  the  two  forms,  but  there  seem  to  exist  inter- 
mediary forms.  The  position  of  the  neutral  point  is,  moreover,  not 
constant,  even  for  the  same  individual :  it  is  displaced  a  little  towards 
the  blue  when  we  increase  the  brightness  of  the  spectrum  (Preyer). 

There  have  been  described  some  very  rare  cases  of  anomalies  of  color 
vision,  which  are  usually  classified  under  the  name  of  akyanopsia  (Blau- 
blindheit).  In  these  cases  the  neutral  point  would  be  found  in  the  yellow- 
green,  and  the  spectrum  would  be  seen  shortened  at  its  blue  extremity. 
But  the  existence  of  this  form  is  far  from  being  established.  In  cases 
of  poisoning  with  santonine,  we  meet  anomalies  of  color  vision  which 
are  somewhat  in  accord  with  these  observations,  but  these  phenomena 
seem  rather  to  be  attributed  to  a  slight  transient  coloration  of  the 
vitreous  body. 

In  consequence  of  the  deficiency  of  their  chromatic  system,  the  dal- 
tonists  are  often  exposed  to  errors,  which  are  especially  striking  when 
they  confound  red  with  green.  This  is  why  Dalton  used  to  walk  in  the 
street  with  the  scarlet  cloak  of  the  Oxford  doctors,  thinking  that  it  was 
black  or  gray.  Cherries  seem  to  them  of  the  same  color  as  the  leaves  of 
the  cherry  tree,  etc.  To  understand  these  errors  we  must  recollect 
that  the  colors  of  objects  are  never  pure;  they  always  contain  white, 
and  this  is  why  red  objects  appear  gray  and  not  almost  black  like  the 
red  of  the  spectrum.  In  spite  of  these  errors  it  is  often  astonishing  to 
see  how  the  daltonists  know  how  to  overcome  their  defect  by  making 
use  of  the  differences  which  the  colors  present  to  them.  Comparing, 
for  example,  red  with  yellow,  they  can  frequently  give  their  true  names 
to  these  colors.  The  hue  for  both  is  the  same,  but  the  red  appears  to 
them  less  pure  than  the  yellow,  and  they  know  that  this  less  pure  yellow 
is  what  is  generally  called  red.  They  generally  seem  more  sensitive  to 
differences  of  brightness  than  normal  persons  do,  and  they  can  some- 


THE  COLOR  8EN8E  269 

times  see  traces  of  color  which  the  normal  eye  does  not  discover.  Thus 
Mauthncr  relates  a  case,  in  which  the  daltonist  claimed  that  he  saw 
yellow  on  a  sheet  of  black  paper.  On  examining  the  paper  it  was  found 
that  it  really  did  reflect  a  little  of  the  yellow  light,  which  had  escaped 
the  normal  observer. 


111.  Monochromasia.  —  There  exists  yet  another  anomaly  of  the  color 
sense,  which  is  very  rare,  but  seemingly  well-established,  namely  mono- 
chromasia.    While  color-blindness  implies  no  other  abnormality,  mono- 
chromatic eyes  manifest  all  other  signs  of  weakness :  photophobia,  albin- 
ism, diminution  of  the  visual  acuity,  etc.    For  these  people  differences 
of  color  do  not  exist;  the  only  differences  they  perceive  are  differences 
of  brightness,  almost  as  on  an  engraving.     The  whole  color  table  is 
narrowed  to  a  point.    The  spectrum  seems  to  them  simply  a  luminous 
band,  the  brightness  of  which  reaches  its  maximum,  not  in  the  yellow 
as  is  the  case  with  the  normal  eye,  but  in  the  green  (at  about  0.52^). 
Bering  emphasized  the  analogy  which  exists  between  the  manner  in 
which  monochromatics  see  the  spectrum,  and  the  appearance  which  it 
presents  to  the  normal  eye  when  its  brightness  is  very  feeble. 

112.  Clinical  Examination  of  the  Color  Sense.  —  The  method  of  mixing 
colors  forms  the  fundamental  examination  of  the  color  sense,  and  we 
can  scarcely  pass  it  over  if  we  desire  to  form  an  exact  idea  of  the  chro- 
matic system  of  the  person  whom  we  observe;  but  the  method  is  too 
complicated  for  clinical  use,  and  it  is,  besides,  completely  dependent  on 
the  good  faith  of  the  person  whom  we  examine.   For  the  clinician  it  is 
important  to  be  able  to  decide  quickly  and  surely  whether  his  client  is 
a  dichromatic  or  not.    With  this  object  in  view  different  methods  have 
been  invented. 

It  must  first  be  noted  that  we  obtain  only  little  useful  information  by 
asking  a  color-blind  person  how  he  would  term  the  color  of  such  and 
such  an  object.  If  we  present  red  to  him,  for  example,  it  may  not  un- 
likely happen  that  he  will  designate  this  color  as  red,  although  he  does 
not  see  it  different  from  certain  greens. 

The  method  most  used  is  the  test  with  colored  yarns  (Holmgren).  We 
present  to  the  subject  the  green  shade  of  least  purity  and  we  request  him 
to  find  the  shades  which  resemble  the  latter,  adding  that  they  may  be  a 
little  more  or  a  little  less  pronounced.  Besides  green  shades,  the  dal- 
tonist matches  yellow  grays,  brown  grays,  red  grays  and  pure  grays. 
We  then  present  to  him  pure  purple.  It  is  here  that  the  alleged  differ- 


270  PHYSIOLOGIC  OPTICS 

ence  between  the  two  kinds  of  daltonists  becomes  apparent.  A  person 
affected  with  anerythropsia  would  find  that  the  blue  and  violet  hues 
resemble  pure  purple,  while  a  person  affected  with  achloropsia  would 
select  the  green  and  gray  shades.  Individuals  who  have  only  an 
incomplete  color-blindness  would  stand  the  latter  test,  but  not  the 
former.  Krenchel,  Daae  and  others  arranged  colored  yarns  in  the  form 
of  charts;  Cohn  used  colored  powders:  Seebeck,  who  invented  the 
method,  used  colored  papers. 

On  the  tables  of  Stilling  are  arranged  a  great  number  of  spots  of  two 
colors,  selected  so  as  to  be  seen  alike  by  the  daltonist.  There  are,  for 
example,  on  one  sheet  complementary  spots,  red  and  green ;  the  .reds 
are  arranged  between  the  greens  so  as  to  form  numbers  visible  to  the 
normal  eye,  but  invisible  to  the  dichromatic  eye,  which  sees  all  the  spots 
of  the  same  color.  The  tables  of  Stilling  do  not  seem  very  good;  it 
appears  that  there  are  daltonists  who  read  them,  and  normal  eyes  which 
do  not  read  them.  The  tables  of  Pfluger,  which  I  have  already  men- 
tioned, are  preferable;  they  are  based  on  a  phenomenon  of  contrast. 
The  patient  looks  at  a  purple  sheet  on  which  are  printed  gray  letters ; 
the  whole  is  covered  with  tissue  paper.  A  normal  eye  sees  the  purple 
ground  through  the  tissue  paper,  and  easily  reads  the  letters  which 
appear  by  contrast  in  the  complementary  color.  The  daltonist  sees  the 
ground  gray  like  the  letters,  so  that  he  cannot  distinguish  the  latter. 

We  can  prove  that  the  anomaly  is  not  feigned  by  making  the  patient 
look  through  a  colored  glass.  If  the  patient  confounds  green  and  red 
he  should  no  longer  confound  them  when  looking  through  a  red  glass, 
for,  as  the  green  rays  do  not  pass  through  this  glass,  the  green  must 
appear  to  him  much  darker  than  the  red.  Daltonists  who  need  to  be 
able  to  distinguish  colors,  chemists  for  example,  may  sometimes  use 
with  advantage  a  colored  glass,  which  puts  them  in  a  position  to  dis- 
tinguish between  two  colors  which  they  otherwise  confound. 

Polarization  instruments  have  been  used  to  discover  color-blindness ; 
Rose  constructed  the  first  instrument  of  this  character ;  the  leucoscope  of 
Kcenig  is  founded  on  the  same  principle.  The  best  of  these  instruments 
is  the  chromatoptometer  of  Chibret.  If  we  place  a  plate  of  quartz  cut 
parallel  to  the  axis  between  two  Nicols,  parallel  to  each  other  and  form- 
ing an  angle  of  45°  with  the  axis  of  the  quartz,  we  see  the  plate  tinted  a 
certain  color  which  depends  on  the  thickness  of  the  quartz.  Making 
the  Nicol  nearest  the  eye  (the  analyzer)  rotate  around  the  axis  of  the 
tube,  the  color  becomes  less  and  less  pure.  At  45°  the  field  is  white,  and 
if  we  continue  to  rotate  the  Nicol  we  obtain  the  complementary  color, 


THE   COLOR  SENSE  271 

which  increases  the  purity,  up  to  90°,  when  it  attains  its  highest  point. 
Replacing  the  analyzer  by  a  double  refracting  crystal,  a  plate  of  spar, 
for  example,  which  acts  like  two  Nicols,  perpendicular  to  each  other, 
the  field  is  seen  double  and  one  of  the  images  of  the  field  has  the  color 
complementary  to  that  of  the  other.  Rotating  the  spar,  the  colors  be- 
come less  and  less  pure,  and  at  45°  the  two  fields  are  white.  The  hues 
of  the  two  complementary  colors  depend  on  the  thickness  of  the  plate 
of  quartz.  In  the  instrument  of  Chibret,  by  placing  the  plate  more  or 
less  obliquely,  we  can  use  a  greater  or  less  thickness,  and  thus  obtain 
the  whole  gamut  of  colors.  The  instrument  thus  presents  a  very  great 
number  of  hues  and  degrees  of  purity. 

The  patient  looks  towards  a  window  through  the  instrument.  We 
place  the  index  of  purity  ES  (fig.  168),  which  regulates  the  position  of 
the  doubly  refracting  crystal,  at  5°,  which  gives  colors  strongly  mixed 
with  white,  and  after  having  put  the  index  of  the  hues  E  G,  which  regu- 
lates the  inclination  of  the  quartz  on  the  orange,  at  zero,  we  ask  the 
patient  if  the  fields  are  alike.  If  they  are  not,  we  rotate  the  index  of  the 


ESL 


Fig.  168.—  Chromatoptometer  of  Chibret. 


hues  slowly  towards  the  red,  yellow  and  violet.  If  the  patient  always  sees 
the  two  fields  different  we  repeat  the  experiment  after  having  placed 
the  index  of  purity  at  zero,  which  makes  the  two  fields  white.  He  ought 
now  to  see  them  alike.  If  the  patient  stands  these  tests,  he  is  not  color- 
blind. If,  on  the  contrary,  in  the  first  experiment  he  sees  the  two  fields 
alike  for  a  certain  hue,  he  is  color-blind.  We  then  increase  more  and 
more  the  purity  of  these  hues.  If  we  thus  succeed  in  producing  a  differ- 
ence between  the  two  fields  the  daltonism  is  incomplete ;  in  the  contrary 
case,  it  is  complete. 

If  there  is  question  of  persons  who  desire  a  certificate  to  be  em- 


272  PHYSIOLOGIC  OPTICS 

ployed  on  railroads,  or  as  sailors,  etc.,  it  may,  in  addition,  be  useful  to 
examine  whether  they  can  distinguish  signals.  An  aperture  of  3  milli- 
meters diameter  in  a  screen,  covered  with  white  paper,  and  illuminated 
from  behind  by  a  lamp,  suffices  for  this  examination.  We  place  the 
person  to  be  examined  at  5  or  6  meters  distance,  and  we  see  whether  he 
commits  errors  when  we  place  glasses  of  different  colors  before  the 
aperture. 

113.  Hypotheses  on  the  Mechanism  of  Color  Vision.  —  To  explain  the 
mechanism  of  color  vision  different  hypotheses  have  been  tried :  the  old 
ones  were  without  any  anatomical  basis;  the  more  recent  have  been 
more  or  less  inspired  by  the  discovery  of  the  retinal  purple.  None  of 
these  hypotheses  are  satisfactory  in  character,  and  the  facts  known  up 
to  the  present  do  not  seem  yet  sufficient  to  explain  the  mechanism  of 
color  vision.  Let  us  mention  briefly  these  hypotheses. 

THEORY  OF  YOUNG.  —  The  following  is  how  Young  explained  his 
hypothesis :  "It  is  certain  that  we  can  produce  a  perfect  sensation  of 
yellow  and  blue  by  a  mixture  of  green  and  red  light  and  of  green  and 
violet  light.  There  are  reasons  for  supposing  that  these  sensations  are 
always  composed  of  a  combination  of  separate  sensations.  This  sup- 
position at  least  simplifies  the  theory  of  colors ;  we  may,  therefore,  accept 
it  with  advantage  until  such  time  as  we  shall  find  it  incompatible  with 
some  phenomenon.  We  shall  proceed,  therefore,  to  consider  white 
light  as  composed  of  a  mixture  of  three  colors  only,  red,  green  and  violet." 

According  to  this  hypothesis,  we  suppose  each  nervous  fibre  of  the 
retina  composed  of  three  fibres  of  the  second  order ;  each  of  these  three 
fibres  would  be  provided  with  a  special  terminal  organ  (a  photo-chemical 
substance)  and  also  with  a  special  central  organ.  An  irritation  of  the 
first  fibre  would  produce  a  red  sensation,  an  irritation  of  the  second  fibre 
a  green  sensation  and  an  irritation  of  the  third  a  violet  sensation.  These 
three  colors  are  termed  principal  colors.  An  irritation  of  the  first  two 
fibres  would  produce  yellow,  etc.  An  irritation  at  once  of  the  three 
fibres  produces  white,  and  if  none  of  the  fibres  is  irritated,  we  have  the 
sensation  of  black.  The  red  rays  irritate  the  first  fibre,  the  green  rays 
the  second,  the  violet  rays  the  third;  the  yellow  rays  irritate  the  first 
and  second,  and  so  forth.  Young  explained  color-blindness  by  sup- 
posing that  one  of  the  fibres  was  wanting.  —  One  of  the  advantages  of 
this  hypothesis  is  that  we  can  suppose  the  action  identical  in  the  three 
fibres.  The  action  in  the  terminal  organs  must  necessarily  be  different, 
but  the  one  in  which  the  impression  is  conducted  to  the  brain  may  be 


THE  COLOR  SENSE  273 

the  same  in  the  three  cases.  The  difference  between  the  three  sensa- 
tions would  be  produced  by  the  different  reaction  of  the  central  organs. 

In  this  form  the  theory  is  very  attractive,  but  does  not  accord  with 
observations  on  color  vision.  It  requires,  indeed,  that  we  can  select 
three  spectral  colors  so  as  to  be  able  to  reproduce  all  existing  hues  and 
degrees  of  purity  by  mixing  them.  But  we  have  seen  that  this  is  not 
possible;  there  always  remain  some  of  the  spectral  colors  which  are 
purer  than  the  mixtures.  According  to  Young  the  color  table  must  have 
an  exactly  triangular  form,  but  the  observations  of  Maxwell  have  shown 
that  this  is  not  the  case.  We  cannot  use,  for  example,  the  standard  colors 
of  Maxwell  as  principal  colors,  because  we  cannot  reproduce  with  them 
the  colors  situated  outside  of  the  triangle. 

MODIFICATION  OF  THE  THEORY  OF  YOUNG  BY  HELMHOLTZ.  —  We 
must,  therefore,  suppose  that  the  sensations  corresponding  to  the  prin- 
cipal colors  are  still  purer  than  the  spectral  colors,  for  then  their  mix- 
tures could  have  the  same  purity  as  the  latter.  On  the  table  the  principal 
colors  would  then  be  placed  farther  from  the  center  than  the  spectral 
colors,  so  that  the  triangle,  which  we  would  obtain  by  joining  them, 
would  complete  the  entire  curve. 

Helmholtz  supposed  that  each  spectral  color  irritated  the  three  fibres 
at  once,  but  in  a  different  degree.  Thus  the  red  rays  would  irritate  the 
first  fibre  strongly,  the  other  two  feebly.  The  impression  produced  by  the 
spectral  red  would  already  contain  white.  Helmholtz  remarked,  in  this 
regard,  that  this  impression  is  not  the  purest  sensation  of  red  that  we 
can  have.  If  we  first  produce  an  after-image  of  an  object  of  the 
complementary  color,  before  looking  at  the  spectral  red,  the  impression 
becomes  much  more  vivid,  because  we  would  thus  have  fatigued  the 
two  other  fibres. 

Helmholtz  at  first  tried  to  explain  color-blindness,  as  Young  did,  by 
the  absence  of  one  of  the  fibres.  He  supposed,  therefore,  three  kinds 
of  color-blindness :  anerythropsia,  achkropsia  and  akyanopsia.  As  we  have 
seen,  the  last  form  is  very  doubtful,  and  the  first  two  seem  to  become 
blended  into  one.  But,  there  are  yet  other  difficulties.  Persons  who  are 
color-blind  declare  that  they  see  yellow  or  blue  in  the  spectrum,  while, 
according  to  Helmholtz,  they  should  see  green  and  violet  or  red  and 
violet.  The  hypothesis  was  saved  by  saying  that  it  was  not  possible  to 
know  what  they  meant  to  convey  by  blue  and  yellow,  but  as  this  explana- 
tion became  very  doubtful,  after  the  observation  of  Hippel,  the  hypothesis 
was  modified  once  more  by  supposing  that  color-blind  persons  possess 
three  fibres,  but  that  in  them  the  colors  act  equally  on  two  of  the  fibres. 


274  PHYSIOLOGIC   OPTICS 

If,  for  example,  the  red  rays  act  as  much  on  the  first  as  on  the  second 
fibre,  they  must  produce  a  yellow  sensation.  It  is  the  same  for  green 
rays.  Taking  the  blue  as  the  third  principal  color,  we  could  thus  ex- 
plain the  manner  in  which  color-blind  people  see  the  colors ;  but  all  these 
modifications  do  not  add  to  the  plausibility  of  the  hypothesis. 

THEORY  OF  HERING.  —  This  scientist  assumes  a  "visual  substance" 
which  is  a  mixture  of  three  others :  one,  which  determines  the  sensation 
of  black  and  white,  another,  which  determines  that  of  red  and  green,  and 
a  third,  which  determines  that  of  yellow  and  blue.  The  red  light  acts  on 
the  red-green  substance,  causing  a  katobolic  change  (disassimilation) 
which  produces  the  sensation  of  red.  The  green  light,  on  the  contrary, 
would  cause  an  anabolic  change  in  this  substance  by  its  action  (assimila- 
tion) which  would  produce  the  sensation  of  green.  The  same  takes  place 
in  the  case  of  the  yellow  and  blue  rays  in  relation  to  the  yellow-blue 
substance.  The  intermediary  rays  act  on  the  two  substances  alike.  But 
all  the  rays  act  on  the  whitish-black  substance,  which  Bering  expresses 
by  saying  that  these  rays  have  besides  their  color  value  (Vaknz),  a  white 
value  (Vaknz)  also.  It  is  not  only  the  white  light,  but  also  the  colored 
rays,  which  disassimilate  this  substance.  If  the  two  other  substances 
did  not  exist,  all  the  rays  would  produce  a  white  sensation,  but  of  differ- 
ent brightness.  This  is  what  takes  place  in  the  case  of  monochromatics 
(achromatics).  If  only  one  of  the  two  substances  is  wanting  we  have 
the  dichromatic  system. 

Hering  supposes,  therefore,  four  principal  colors:  red  and  green, 
yellow  and  blue,  and  he  thinks  that  we  have  a  direct  impression  of  the 
fact  that  these  four  colors  are  pure,  and  that  the  others,  perceived  by 
an  action  on  the  two  substances  together,  are  compound. 

The  rivalry  between  these  two  theories,  the  first  of  which  was  inspired 
by  observations  on  mixtures  of  colors,  whilst  the  second  seems  to  be 
derived  especially  from  the  study  of  after  images,  has  formed  the  sub- 
ject of  a  great  number  of  works ;  the  pupils  of  Helmholtz  tried  to  prove 
that  the  hypothesis  of  Hering  was  false,  and  vice  versa.  It  seems  to  me 
that  both  theories  have  suffered  by  it.  The  theory  of  Hering  seems 
rather  to  give  a  statement  of  known  facts,  than  to  explain  them.  It  is 
based  on  the  fact,  which  it  seems  to  me  difficult  to  deny,  that  the  human 
eye  does  not  see  any  resemblance  between  the  four  principal  colors  of 
the  spectrum,  red,  yellow,  green  and  blue,  while  each  of  the  interme- 
diary colors  resembles  two  of  the  principal  colors.  But  it  must  be  noted 
that  the  red  of  Hering  ought  to  be  complementary  to  the  green ;  it  does 
not  correspond,  therefore,  to  the  spectral  red,  which,  according  to 


THE  COLOR  SENSE  275 

tiering,  already  contains  yellow,  but  to  a  purple  color  which  we  cannot 
readily  claim  to  give  the  direct  impression  of  a  pure  color,  (i)  It  seems 
to  me  also  that  a  theory  which  renders  no  account  of  the  special  situa- 
tion of  the  yellow  among  the  colors,  is  necessarily  insufficient. 

OTHER  THEORIES.  —  Among  the  more  recent  theories,  we  may  cite 
that  of  Ebbinghaus,  who  supposes  the  existence,  in  the  cones,  of  a  green 
substance,  the  decomposition  of  which  would  produce  the  sensation  of 
red  and  green,  while  the  purple,  by  its  decomposition,  would  produce 
the  sensation  of  yellow  and  blue.  Parinaud  supposes  that  stimulation 
of  the  rods  produces  a  sensation  of  non-colored  light,  while  stimulation 
of  the  cones  may  produce  all  possible  sensations,  the  sensation  of  colors 
and  the  sensation  of  white.  The  retina  would  have  two  systems  sensi- 
tive to  light,  one  monochromatic,  the  other  trichromatic.  The  ideas  of 
v.  Kries  almost  agree  with  those  of  Parinaud. 

Arthur  Kcenig  exploited  a  theory  which  may  be  considered  as  a  devel- 
opment of  the  theory  of  Young-Helmholtz.  He  supposes  the  red,  green 
and  blue  as  principal  colors.  According  to  Kcenig,  the  decomposition 
of  the  retinal  purple  into  yellow  produces  the  weak  sensation  of  gray, 
which  causes  any  color  when  it  is  sufficiently  weak.  Further  decompo- 
sition produces  the  sensation  of  blue.  Perception  of  the  two  other 
principal  colors,  green  and  red,  is  effected  by  the  agency  of  the  pigment 
cells,  while  the  cones  must  be  considered  as  dioptric  instruments  in- 
tended to  concentrate  the  light  on  the  epithelial  layer.  —  I  have  already 
mentioned  that  H.  Miiller  measured  the  distance  of  the  retinal  vessels 
from  the  sensitive  layer  by  means  of  the  parallax  of  the  vessels,  seen 
entoptically  (see  page  153).  In  collaboration  with  Zumft,  Kcenig  re- 
peated these  experiments  with  spectral  light.  He  found  that  the  distance 
increases  according  as  we  approach  the  red  end  of  the  spectrum.  The 
layer  sensitive  to  green  light,  and  especially  that  sensitive  to  red  light, 
would,  therefore,  be  situated  behind  the  layer  sensitive  ta  blue.  The 
distance  of  these  two  layers  exceeded  even  the  retinal  thickness,  which 
led  Kcenig  to  suppose  that  the  perception  of  these  two  colors  takes  place 
in  the  epithelial  layer.  —  These  experiments  still  need  to  be  verified; 
Koster  repeated  them  without  success. 

Bibliography.  —  In  spite  of  the  great  number  of  works  on  color  vision,  this  question 
still  seems  imperfectly  elucidated.  In  the  preface  to  his  treatise  on  light  which  appeared  a 
few  years  before  Newton's  works  on  optics,  Huyghens  said  he  would  not  speak  of  colors,  "  a 
question  in  which,  up  to  the  present,  no  one  can  pride  himself  on  his  success."  It  seems 


(1)  Towards  the  periphery  of  the  visual  field  there  exists  a  dichromatic  zone,  in  which  we  see  only 
yellow  and  blue  colon.  A  red  object  seems  yellow  at  this  place,  while  a  purple  color  appears  blue :  it 
is  the  intermediary  tint  which  corresponds  to  the  red  of  Hering. 


276  PHYSIOLOGIC  OPTICS 

to  me  that  this  phrase,  which  was  true  at  the  time  of  Huyghens  as  to  the  physics  of  colors, 
may  be  applied  to-day  to  their  physiology.     This  subject  has  not  yet  found  its  Newton. 

Newton  (I.).  Optics.  London,  1704. —  Lambert.  Farbenpyramide.  Augsburg,  1772. — 
Dalton,  Edinburgh.  Philos.  Journal.  Vol.  VI.  —  CEuvres  de  Young,  edited  by  Tscherning, 
p.  217-232.  —  Purkinje.  Zwr  Physiologie  der  Sinne.  II,  p.  109,  1825.  —  Seebeck.  Ueber  den 
bei  manchen  Personen  vorkommenden  Mangel  an  Farbensinn.  Pogg.  Ann.,  1837,  p.  177.  — 
Helmholtz  (H.).  Ueber  die  Theorie  der  zusammengesetzten  Farben.  Pogg.  Ann.,  1852,  p.  45. 

—  Helmholtz  (H.).    Ueber  die  Zusammensetzung  der  Spectralfarben.    Pogg.   Ann.,  1855,  p.  1. 

—  Helmholtz  (H.).    Ueber  die  Empjindlichkeit  der  menschlichen  Netzhaut  fur  die  brechbarsten 
Strahlen  des  Sonnenlichts.  Pogg.  Ann.,  1855,  p.  205.  —  Maxwell  (C.).  Experiments  on  Colors  as 
Perceived  by  the  Eye  with  Remarks  on  Color  Blindness.  Transact,  of  the  Roy.  Soc.  ofEdinb. ,  XXI, 
1855.  — Maxwell  (C.).   On  the  Theorie  of  Compound  Colors  and  the  Relations  of  the  Colors  of  the 
Spectrum.  Phil,  trans.,  I860.  —  Maxwell  (C.).  On  the  Unequal  Sensibility  of  the  Foramen  Centrale 
to  Light  of  Different  Colors.   Edinb.  Journ.,  1856,  IV,  p.  337.  —  Hering  (E.).  in  Lotos  Prag. 
1880-82-85-87.  —  Rayleigh.    Nature.   Vol.  XXV,  p.  64,  1881.  —  Mac£  de  Lepinay  and 
Nicati.  Ann.  de  chimie  et  de  physique.   Ser.  5,  t.  24,  p.  289,  1881  et  t.  30,  p.  145,  1883.  - 
Uhthoff  ( W.).    Ueber  das  Abhdngigkeitsverhdltniss  der  Sehschdrfe  von  der  Beleuchtungsintensitdt. 
Grafes  Arch.  XXXII,  1886.  —  Uhthoff  (W.).    Weitere  Untersuchungen  uber  die  Abhdngigkeit 
der  Sahscharfe  von  der  Intensitdt  sowie  von  der  Wellenldnge  im  Spektrum.  Grafes  Arch.  XXXVI, 
1890.  —  Kriess  (I.  v.).   Die  Gesichtsempfindungen  und  ihre  Analyse.   Leipzig,  1882.  —  v.  Hip- 
pel.    Grafes  Archiv.  XXVII,  3,  p.  47.  1881.  —  Krenchel  ( W.).    Ueber  die  Bypothesen  von 
Grundfarben.     Grafes  Arch.   XXVI,  p.  91,   1880.  —  Kcenig  u.  Brodhun.     Experimented 
Untersuchungen  uber  die  psychophysische  Fundamentalformel  in  Bezug  auf  den  Gesichlssinn. 
Acad.  of  Berlin,  July  26,  1888,  and  June  27, 1889.  —  Kcenig  (A.)  and  Dieterici  (C.).  Die 
Grundempjindungen  in  normalen  und  anomalen  Farbensystemen  und  ihre  Intensitdtsvertheilung  im 
Specfrum.  Zeitschrift  fur  Psychol.,  IV.,  p.  241,  1892.  —  Kcenig  (A.)  et  Zumft  (I.).    Ueber 
die  lichtempfindliche  Schicht  in  der  Netzhaut  des  menschlichen  Auges.  Acad.  of  Berlin,  1894,  May 
24.  —  Kcenig  (A.).     Ueber  den  menschlichen  Sehpurpur  und  seine  Bedeutung  fur  das  Sehen. 
Acad.  of  Berlin,  1894,  June  21.  —  Chibret.  Chromatoptometre.  Bulletin  de  la  Soc.  fr.  d'opht., 
1836,  p.  336.  — Ebbinghaus  (H.).    Theorie  des  Farbensehens.   Hamburg,  1893.  —  Parinaud 
(H.).  La  sensibUite  de  Vceil  nux  couleurs  spectrales;  fonctions  des  elements  retiniens  et  du  pourpre 
visuel.  Ann.  d'oc.  t.  CXII,  p.  228,  1894.  —  Koster  (W.).    Ueber  die  percipirende  Schicht  der 
Netzhaut  beim  Menschen.  Grafes  Arch.,  LXI,  1,  p.  1,  1895. 


CHAPTER   XVIII. 
THE  FORM  SENSE 

114.  Central  Visual  Acuity.  —  The  power  of  distinguishing  forms  is  a 
very  complex  faculty,  which  is  in  great  part  connected  with  the  ocular 
movements.  To  judge  of  the  form  of  objects  we  grope  for  them,  so  to 
speak,  with  the  look.  Nevertheless,  indirect  vision  furnishes  an  idea  of 
the  form  of  objects.  According  to  empiric  ideas  (page  219)  it  would  be 
the  observations  made  during  the  displacements  of  the  look  that  would 
have  taught  us  the  meaning  of  the  impressions  obtained  in  indirect 
vision. 

The  lowest  angle  under  which  two  points  can  be  distinguished  from 
each  other  has  been  taken  as  the  measure  of  the  form  sense.  Astron- 
omers for  a  long  time  devoted  attention  to  this  question.  Hooke,  for 
instance,  said  that  in  order  that  a  double  star  can  be  recognized  as  such 
by  the  eye,  the  interval  must  correspond  to  one  minute,  and  moreover, 
that  good  eyes  would  be  necessary  to  see  two  stars  under  these  condi- 
tions. Later,  the  physiologists  took  up  the  question,  generally  by  work- 
ing with  a  small  grating  the  bars  and  intervals  of  which  were  of  the 
same  size.  We  place  the  grating  towards  the  sky  and  try  how  far  we 
can  move  away  from  it  before  the  bars  become  confused.  Care  must 
be  taken  that  the  image  formed  on  the  retina  is  distinct,  by  correcting 
defects  of  refraction,  if  there  are  any.  In  accord  with  most  observers 
Helmholtz  found  nearly  the  same  angle  as  Hooke,  that  is  to  say,  one 
minute,  but  it  must  be  observed  that  it  is  neither  the  width  of  a  bar  nor 
that  of  the  interval,  but  the  sum  of  the  two,  which  corresponds  to  this 
angle. 

Considering  the  anatomical  structure  of  the  retina,  we  would  expect 
that  the  angle  of  least  distinction  would  correspond  to  the  size  of  a 
cone.  In  the  experiment  of  Hooke  we  may  suppose,  indeed,  that  we 
can  distinguish  two  stars  if,  between  the  two  cones  on  which  their 
images  are  formed,  there  is  found  a  third,  which  does  not  receive  any 

277 


278 


PHYSIOLOGIC  OPTICS 


impression  (fig.  169).  We  may,  therefore,  conclude  that  the  angular 
size  of  a  cone  must  be  smaller  than  the  angular  distance  separating  the 
two  stars.  In  the  experiment  of  Helmholtz,  on  the  contrary,  we  cannot 
conclude  that  the  size  of  the  cone  must  be  smaller  than  the  angular 
size  of  the  black  bar ;  for  we  can  very  well  imagine  a  larger  cone,  the 
central  part  of  which  may  be  occupied  by  the  image  of  the  black  bar, 
while  the  lateral  parts  would  be  occupied  by  a  part  of  the  images  of  the 
intervals,  but  which  would  receive,  however,  less  light  than  the  neigh- 


Fig.  169. 

Experiment  of  Hooke. 

The  images  of  two  stars 
(e,  e)  are  formed  on  two 
cones  separated  by  a  third. 


Fig.  170. 
Measurement  of  the  visual 

acuity  by  a  grating, 
aa,  Images  of   the   bars 
separated  by  those  of  the 
intervals,  bb. 


Fig.  171. 
Measurement  of  the  visual 

acuity  with  a  grating. 

Limit.  —  All  the  cones 
receive  the  same  impres- 
sion. 


boring  cones  (fig.  170).  But  we  can  conclude  that  the  cone  must  be 
smaller  than  the  angular  distance  separating  the  centers  of  the  two 
neighboring  luminous  intervals  (or,  which  amounts  to  the  same  thing, 
smaller  than  the  sum  of  the  black  bar  and  a  luminous  interval),  for  if 
the  size  of  the  cones  were  equal  to  this  distance,  all  the  cones  would 


Fig.  172.  —  Experiment  of  Hooke,  the  optics  of  the  eye  being  defective.  Instead  of  distinct 
images  the  stars  form  diffusion  spots  ee,  ee. 

receive  the  same  quantity  of  light  (fig.  171),  and  the  bars  would  be  con- 
fused. Thus  the  result  obtained  by  Helmholtz  is  in  agreement  with  that 
of  Hooke. 

Placing  the  distance  of  the  nodal  point  of  the  eye  from  the  retina  at 

15  mm.  the  angular  size  of  a  minute  corresponds  to  6(yL  36Q  =  0.004  mm- 
In  the  fovea  the  size  of  the  cones  is  about  0.002  mm.  The  visual  acuity 
does  not  seem,  therefore,  to  altogether  reach  the  degree  which  we 


THE  FORM  SENSE  279 

would  expect  according  to  the  structure  of  the  retina,  probably  on 
account  of  optic  irregularities.  It  seems  rare,  indeed,  that  a  luminous 
point  forms  its  image  on  a  single  cone,  and  if  it  extends  over  several 
cones,  it  is  not  strange  that  the  angle  of  least  distinction  is  larger  than 
the  angular  size  of  a  cone  (fig.  172). 

One  might  think  that  the  least  angle  of  visibility  may  serve  as  a 
measure  of  the  form  sense,  that  is  to  say,  that  we  can  measure  it  by 
determining  what  is  the  smallest  visual  angle  under  which  an  object 
may  be  seen;  but  it  is  evident  that  this  angle  depends  solely  on  the 
luminous  intensity  of  the  object,  for,  in  spite  of  their  minimum  angular 
size,  we  see  fixed  stars  very  well  when  they  are  sufficiently  luminous. 

If  the  eye  were  optically  perfect,  so  that  the  image  of  the  star  could 
be  formed  on  the  surface  of  a  single  cone,  it  is  easy  to  see  that  the 
luminous  impression  which  this  cone  may  receive,  if  it  be  sufficiently 
strong,  would  suffice  to  make  the  object  visible,  even  if  the  image  did 
not  occupy  the  entire  surface  of  the  cone.  But,  as  a  rule,  the  optic 
properties  of  the  eye  are  not  so  good.  Most  people  do  not  see  the  stars 
as  points,  but  as  small  surfaces  so  much  greater  in  proportion  as  the 
star  is  brighter;  the  image  of  the  star  is,  indeed,  a  circle  of  diffusion 
composed  of  more  or  less  luminous  parts :  when  the  light  is  feeble  these 
latter  parts  disappear  so  that  the  star  appears  smaller.  As  long  as  the 
star  is  luminous  the  image,  therefore,  generally  covers  several  cones; 
if  the  light  diminishes  the  image  may  be  formed  on  a  single  cone,  but 
the  visibility  always  depends  on  the  brightness  only.  A  comparison  with 
the  preceding  experiment  shows  also  that  we  cannot  use  the  visibility 
of  a  single  star  as  a  measure  of  visual  acuity ;  the  experiment  would  be 
identical  with  that  of  the  grating,  if  we  imagine  two  infinitely  large  bars 
separated  by  an  interval  corresponding  to  the  star.  We  have  seen  that 
we  may  conclude  that  the  angular  size  of  the  cone  is  smaller  than  the 
angular  size  of  a  bar  plus  an  interval ;  but  this,  in  the  present  case,  has 
no  application. 

In  clinics  we  use,  for  the  measurement  of  visual  acuity,  the  charts  of 
Snellen  or  others  constructed  on  the  same  principle.  The  letters  are 
arranged  so  as  to  be  seen  under  an  angle  of  5  minutes ;  the  lines  which 
form  the  letters,  as  well  as  most  of  the  intervals  which  separate  them, 
are  seen  under  an  angle  of  i  minute.  We  see  that  the  normal  acuity 
of  Snellen  corresponds  to  half  of  that  which  Helmholtz  found,  with  his 
grating,  in  which  each  bar  and  each  interval  corresponded  to  a  half 
minute.  We  have  found  also  that  the  best  eyes  have  a  visual  acuity  which 
approaches  2  (\  or  -}-)» and  we  can  be  almost  certain  that  if,  with  a  good 


280  PHYSIOLOGIC  OPTICS 

illumination,  the  acuity  is  only  equal  to  I,  the  eye  presents  defects  suffi- 
ciently pronounced  to  be  easily  established. 

We  have  said  that  the  angle  under  which  the  letters  are  seen  cor- 
responds to  5  minutes.  The  angle  being  equal  to  the  linear  size  of  the 
letter  divided  by  the  distance  at  which  it  is  seen,  it  is  clear  that  the 
letters  which  are  intended  to  be  seen  at  a  distance  of  12,  meters  must 
have  double  the  linear  size  of  those  which  are  seen  at  6  meters.  If  the 
former  are  seen  at  a  distance  of  6  meters  only,  we  say  that  the  visual 
acuity  is  equal  to  ~  =  ^ .  Different  authors,  Javal  among  others,  have 
observed  that  this  way  of  designating  the  visual  acuity  is  not  very 
logical,  and  that  we  should,  in  this  case,  say  that  the  acuity  is  equal  to 
J,  since  the  surface  of  the  letter  in  question  is  4  times  greater  than  that 
which  corresponds  to  the  acuity  I. 

In  spite  of  the  theoretical  objections  which  may  be  made  to  it,  the 
chart  of  Snelkn  is,  however,  very  practical.  It  is  certain  indeed,  that 
some  of  the  letters  are  much  more  easily  read  than  others  on  the  same 
line.  The  legibility  of  a  letter  is,  indeed,  a  very  complex  affair,  which 
is  far  from  depending  altogether  on  the  size  of  the  intervals  separating 
the  different  lines.  Attempts  have  been  made  to  remedy  this,  some- 
times by  making  larger  the  letters  which  are  read  with  difficulty,  some- 
times by  selecting  only  letters  which  are  easily  legible.  These  improve- 
ments are  not  widely  employed,  for  they  are  without  much  utility;  by 
using  the  chart  we  learn,  in  fact,  very  quickly  the  degree  of  legibility 
which  each  letter  has  for  a  normal  eye.  A  more  serious  inconvenience 
is  the  small  number  of  large  letters,  which  frequently  renders  the  deter- 
mination of  refraction  difficult  in  cases  in  which  the  acuity  is  not  so 
good,  because  the  patients  learn  the  letters  by  heart.  To  have  a  con- 
stant illumination,  it  is  well  to  place  the  chart  in  a  dark  place  and  to 
illuminate  it  with  a  gas  jet  provided  with  a  reflector,  which  protects  the 
eyes  of  the  patient.  The  chart  of  Javal  is  transparent  and  placed  by  the 
side  of  the  patient,  who  looks  at  it  in  a  looking-glass.  We  thus  achieve 
this  result,  that  the  letters,  being  opaque,  are  always  seen  perfectly 
black,  and  that  the  distance  is  double  by  reflection.  The  size  of  the 
letters  increases  in  geometrical  progression,  which  had  already  been 
proposed  by  Green.  Burchardt  had  printed  series  of  groups  of  dots  of 
different  sizes  arranged  after  the  principle  of  Snellen.  The  patient  must 
be  able  to  count  the  number  of  dots  which  compose  a  group.  Many 
oculists  followed  the  example  of  Snellen  and  constructed  charts  on  the 
same  principle. 

We  still  use  the  reading  test  types  of  Jaeger,  the  first  fairly  complete 


THE  FORM  SENSE  281 

collection  of  characters  of  different  sizes  which  had  been  used.  The 
advantage  which  the  chart  of  Snellen  presents  is  that  it  has  written  upon 
it  the  distance  at  which  the  patient  ought  to  be  able  to  see  each  line, 
which  enables  oculists  to  examine  the  sight  of  all  patients  at  a  like  dis- 
tance. This  principle  had  already  been  applied  by  Stellwag. 

In  1891,  Guillery  proposed  to  measure  the  visual  acuity  simply  by  the 
distance  at  which  we  can  distinguish  a  black  point  on  a  white  ground. 
By  comparisons  with  the  letters  of  Snellen,  he  found  that  a  black  point 
seen  under  an  angle  of  50  seconds  corresponds  to  the  normal  acuity ;  at 
5  meters  it  should  have  a  diameter  of  1.2  mm.  This  point  is  designated 
as  No.  i.  No.  2  has  the  surface  twice  as  large  as  No.  i,  and  the  patient 
who  sees  only  No.  2  at  5  meters  distance,  has  an  acuity  of  J,  etc.  Each 
point  is  on  a  white  square,  sometimes  in  the  center,  sometimes  below, 
sometimes  in  an  angle,  etc.,  and  there  are  on  the  same  line  several  tests 
side  by  side  in  which  the  point  has  the  same  size.  The  patient  must  tell 
at  what  part  of  the  square  he  sees  the  point.  It  seems  that  we  measure 
the  visual  acuity  quite  as  well  in  this  way  as  by  the  principle  of  Snelleny 
which  is  quite  interesting,  and  shows  that  we  cannot  identify  the  exam- 
inations with  the  luminous  point  on  a  black  ground  with  that  made  by 
means  of  a  black  point  on  a  white  ground.  Javal  constructed  a  small 
portable  scale  on  the  same  principle:  it  is  composed  of  small  black 
squares,  such  that  the  side  of  a  square  is  also  equal  to  the  diagonal  of 
the  preceding  one.  If  the  side  is  equal  to  I,  the  diagonal  is  Vl2  +  l2 
=  V2>  which  is  the  side  of  the  following  square;  the  diagonal  of  this 
latter  is  then  2,  and  so  forth.  In  this  manner  the  area  of  a  square  is 
always  double  that  of  the  preceding  square. 

RELATIONS  BETWEEN  VISUAL  ACUITY  AND  ILLUMINATION.  —  The 
visual  acuity  depends  directly  on  the  illumination  of  the  chart,  but  it  is 
quite  difficult  to  determine  the  relation  in  a  general  way,  because  there 
are  many  different  factors  which  affect  it.  Thus  the  relation  must  de- 
pend on  the  pupillary  size,  on  the  manner  in  which  the  pupil  contracts 
under  the  influence  of  light,  on  the  degree  of  optic  perfection  and  espe- 
cially on  the  adaptation  of  the  eye  to  darkness.  Druault  has  made  some 
researches  on  this  question,  by  moving  a  candle  (of  stearine  of  22  mm. 
diameter)  towards  the  visual  acuity  chart,  and  noting  the  distance  at 
which  this  light  would  allow  each  line  to  be  read;  the  eye  was  in  a 
degree  of  medium  adaptation.  In  order  to  obtain  high  degrees  of  illum- 
ination, he  replaced  the  candle  by  a  lamp  equivalent  to  fifty-four  candles. 
The  following  table  shows  his  results,  taking  as  unit  the  illumination 
obtained  by  placing  a  candle  at  a  distance  of  one  meter. 


282  PHYSIOLOGIC  OPTICS 

Illumination.  Acuity. 

0.016  meter  candles  .............................       -^L  =  0.075 

.200 

0.020      "  "      ...........   .................       _yL  =  0.15 

J.UU 

0.028      "  "      .............................       -J5-  =0.21 

0.047      "  "      .............................       -15-  =  0.30 

ou 

0.12       "  "      .............................       -15-  =  0.37 


0.25 


"  " 


30    ' 
0.67       "  "      -||-  =  0.75 

1.50       "  "      -41-  =  1.00 

10 

16.7         "  "      -15-  =  1.25 

5400  "  "      -15-  =  1.50 

We  note  that  the  acuity  increases  rapidly  at  first,  then  slowly,  with 
the  illumination,  and  finally  there  is  need  of  an  enormous  increase  of 
illumination  in  order  to  make  the  acuity  rise  from  1.25  to  1.50.  Still 
increasing  the  illumination,  the  acuity  would  probably  still  increase,  but 
very  little,  so  that  the  curve  indicating  the  visual  acuity  for  the  different 
illuminations  would  be  a  flattened  curve  much  elongated  and  more  or 
less  like  the  curve  of  the  light  sense  (fig.  148). 

I  have  already  observed  that  the  relation  between  the  visual  acuity 
and  the  illumination  depends,  furthermore,  on  the  color  of  the  light 
used  (page  244). 

The  theory  according  to  which  the  layer  of  the  cones  and  rods  would 
be  the  sensitive  layer,  explains  sufficiently  well  the  acuity  which  we 
obtain  with  a  good  illumination,  but  it  gives  by  no  means  a  satisfactory 
explanation  of  the  manner  in  which  the  acuity  falls  when  the  illumina- 
tion diminishes. 

115.  Peripheral  Acuity.  —  We  determine  the  limits  of  the  visual  field 
with  a  perimeter  or  campimeter,  by  allowing  the  person  examined  to 
fix  the  center,  and  finding  up  to  what  limit  the  patient  can  still  see  the 
object  in  indirect  vision.  The  distance  of  the  eye  from  the  plane  of  the 
campimeter,  or  from  the  arc  of  the  perimeter,  varies  slightly  for  differ- 
ent instruments.  The  object  is  generally  a  white  square  (or  a  colored 


THE  FORM  SENSE  283 

one),  the  side  of  which  is  about  I  centimeter.  With  the  white  object 
we  thus  find  the  absolute  limits  of  the  field;  taking  larger  or  brighter 
objects  we  scarcely  obtain  any  more  extended  limits.  It  is  otherwise  for 
the  examination  with  colors.  It  seems,  indeed,  that  by  taking  sufficiently 
large  and  bright  objects  we  obtain  larger  limits  than  by  ordinary  exam- 
ination. In  clinics,  we  examine  generally  with  the  white,  blue,  red  and 
green,  and  we  find,  as  a  rule,  the  field  less  extended  in  the  order  in  which 
I  have  named  the  colors.  If  one  finds  different  limits  for  the  red  and 
green,  this  is  probably  due  to  the  fact  that  colors  which  are  not  com- 
plementary or  which  have  a  different  brightness  are  used.  Otherwise 
we  ought  to  find  the  same  limits. 

The  visual  acuity  falls  greatly  as  soon  as  the  image  is  moved  away 
from  the  fovea.  If,  for  example,  we  fix  the  border  of  the  chart  of  Snellen 
the  acuity  falls  in  consequence  to  J  or  -^-.  Attempts  have  been  made  to 
determine  the  peripheral  acuity  according  to  the  principle  of  Snellen, 
but  the  method  is  very  difficult  to  use  clinically,  whilst  another  method 
introduced  by  Bjerrum  seems  to  give  good  results.  He  simply  repeats 
the  perimetric  examination  with  smaller  and  smaller  objects.  He  uses 
a  distance  of  2  meters,  placing  the  patient  in  front  of  a  large  black  cur- 
tain; the  objects  used  are  small  ivory  discs  of  different  sizes,  fixed  on 
black  rods  of  i  meter  in  length.  The  observer  must  wear  black  gloves. 
By  thus  examining,  Bjerrum  found  as  the  limits  of  the  normal  field : 

Outside.  Inside.  Below.  Above. 

Withadiskof 3mm  35°  30°  30°  25° 

-  6mm  50°  40°  40°  35° 

Normal  limits 90°  60°  70°  60° 

By  this  method  we  can  frequently  establish  defects  which  we  could 
not  otherwise  find.  We  thus  meet  cases  of  atrophy  of  the  optic  nerves, 
in  which  the  field  examined  in  the  ordinary  manner  is  normal,  whilst 
the  method  of  Bjerrum  reveals  considerable  contractions.  In  glaucoma 
Bjerrum  has,  by  his  method,  discovered  scotomata  scattered  in  the  field, 
but  which  are  generally  connected  with  a  spot  of  Mariotte  by  a  lacuna 
in  the  form  of  a  bridge.  The  paracentral  scotoma  is  thus  connected 
with  the  papilla  by  a  lacuna  which  surrounds  the  upper  or  lower  half 
of  the  macula.  Its  form  indicates  directly  the  course  of  the  nerves. 
Sometimes  it  may  be  useful  to  repeat  the  examination  with  diminished 
illumination. 

More  recently,  Groenotuw  has  made  analogous  measurements  with  a 
black  point  on  a  white  ground.  He  designates  as  isopters  the  lines  drawn 
in  the  visual  field  through  the  points  where  the  visual  acuity  is  the  same. 


284  PHYSIOLOGIC  OPTICS 

These  methods  are  founded  on  the  same  principle  which  was  used  by 
Guillery  for  the  measurement  of  central  acuity.  Their  theory  is  still  to 
be  formulated. 

In  the  normal  field  there  is  only  one  interruption,  namely,  the  blind 
spot  which  corresponds  to  the  papilla.  It  was  discovered  by  Mariotte, 
whose  name  it  bears,  and  created  at  the  time  a  very  great  sensation. 
From  his  discovery  Mariotte  drew  this  conclusion,  that  it  is  the  choroid 
which  is  the  sensitive  layer  of  the  eye,  since  it  was  absent  in  this  place, 
and  this  idea  was  for  a  long  time  accepted.  We  can  determine  the  form 
of  the  blind  spot  by  the  ordinary  methods  with  the  perimeter,  and  still 
better  by  placing  ourselves  at  a  distance  of  one  or  two  meters.  The 
spot  has  an  elliptical  form ;  generally  we  succeed,  on  examining  with  a 


Fig.  173. — Mariotte' s  blind  spot  in  my  right  eye,  drawn  by  Holth. 

very  small  object,  in  following  the  big  vessels  a  little  outside  of  the 
papilla  (fig.  173).  If  we  do  not  succeed  in  following  them  farther,  it  is 
due  to  the  lack  of  stability  of  the  fixation.  According  to  the  researches 
of  Dr.  Holth,  who  drew  figure  173,  it  is  almost  impossible  to  maintain 
an  almost  exact  fixation  for  more  than  5  or  6  seconds ;  after  this  time 
the  look  makes  involuntary  deviations  which  may  reach  a  third  or  half 
a  degree,  and  after  20  or  30  seconds  we  frequently  observe  deviations 
which  often  exceed  one  degree.  We  can  control  fixation  by  using  as  the 
object  of  fixation  a  point  marked  on  a  small  colored  surface  on  a  white 
ground.  After  a  very  short  time  we  see  the  surface  surrounded  with  a 


THE  FOKM  SENSE 


285 


border  of  the  complementary  color.  —  The  internal  border  of  the  spot 
of  Mariotte  is  about  12  degrees  from  the  point  of  fixation,  and  the 
diameter  corresponds  to  about  6  degrees,  or  12  times  the  diameter  of 
the  moon. 

PHENOMENON  OF  TROXLER.  —  If  we  draw  several  black  spots  on  a 
sheet  of  paper  and  fix  one  of  them  for  some  time,  we  see  sometimes  one, 
sometimes  another  of  the  surrounding  spots  disappear,  to  reappear  a 
little  while  after,  generally  at  the  moment  of  winking  or  of  making  a 
slight  movement  of  the  eye.  This  singular  phenomenon  which  was 
described  at  the  beginning  of  this  century  by  Troxler,  has  recently  been 


Fig.  174. 

studied  by  Dr.  Holth.  The  color  of  the  background,  as  well  as  that  of 
the  spots,  plays  no  part ;  during  the  disappearance  of  these  latter  we  see 
in  their  place  the  background  only;  the  scotoma  is,  therefore,  filled 
almost  like  the  spot  of  Mariotte.  Even  the  spot  fixed  may  disappear 
after  a  long  period  of  fixation.  In  order  to  study  the  phenomenon  we 
can  observe  a  regular  diagram  as  in  figure  174.  For  my  eye  the  phe- 
nomenon begins  after  having  fixed  the  middle  for  8  or  9  seconds,  that 
is  to  say,  at  the  moment  when  the  fixation  begins  to  be  less  steady. 
From  this  moment  the  figure  shows  continuous  changes:  sometimes 


286  PHYSIOLOGIC  OPTICS 

one  part  of  the  figure  disappears,  sometimes  another.  An  interesting 
fact  is  that  most  frequently  the  scotomata  are  not  absolute :  sometimes 
it  is  the  horizontal  lines  which  disappear  at  one  place,  while  the  vertical 
lines  persist,  sometimes  the  contrary  takes  place.  These  phenomena 
recall  forcibly  that  which  has  been  described  under  the  name  of  antag- 
onism of  the  visual  fields  and  which  we  observe,  for  example,  when  pre- 
senting in  a  stereoscope  horizontal  lines  to  one  eye  and  vertical  lines  to 
the  other.  —  If  we  fix  the  center  of  a  figure  composed  of  concentric 
circles  and  radii,  we  see  sometimes  the  latter,  sometimes  the  circles. 
On  a  chess-board  we  see  sometimes  one,  sometimes  another  of  the 
squares  disappear,  and  so  forth.  Holth  even  caused  luminous  objects  to 
disappear,  the  moon  for  example;  according  to  him  small  objects  dis- 
appear even  if  we  give  them  a  slow  motion.  There  is  reason,  therefore, 
to  be  on  the  guard  against  this  source  of  error,  if  we  wish  to  perform 
perimetry  with  precision. 

Bibliography.  —  Hooke  v.  Smith,  Robert.  Court  complet  d'optique,  translated  by  Peze- 
nas.  Paris,  1767,  p.  44.  —  Troxler.  Ueber  das  Verschwinden  gesehener  Gegenstdnde  innerhalb 
unseres  Gesichtskreiscs.  Himly  u.  Schmidt.  Ophthalm.  BibllotJielc.,  1802,  II,  p.  1.  —  CEuvres  dt 
Young,  edited  by  Tscherning,  p.  78.  —  Stellwag  T.  Carion.  Die  Accommodationsfehler  des 
Auges.  Wien,  1855.  —  Guillery.  Em  Vorschlag  zur  Vereinfachung  der  Sehproben.  Arch.  f. 
Augenheilk.,  XXIII,  p.  323, 1891.  —  Grcenouw.  Ueber  die  Sehschdfe  der  Nelzhautperipherie 
und  eine  neue  Untersuchungsmethode  derselben.  Arch.  f.  Augenheilk. ,  XXVI,  p.  85,  1893.  — 
Bjerrum.  Undersoegelsen  of  Synet.  Copenhagen,  1894.  —  S.  Holth.  Om  det  normale  Synsor- 
gans  Stirreblindhed.  Norsk  Magaeinfor  Laegevidenskaben.  August,  1895. 


BOOK    III 

THE  OCULAR  MOVEMENTS 


AND 


BINOCULAR  VISION 


CHAPTER  XIX. 

THE  LAW  OF  LISTING 

116.  Center  and  Axes  of  Rotation  of  the  Eye.  —  The  movements  of 
the  eye  are  made  freely  in  all  directions;  the  extent  of  the  field  of 
fixation  is  about  55°  in  all  directions.  —  It  is  easy  to  prove  that  the  soft 
parts  which  fill  the  orbit  are  incompressible :  if  we  try  to  push  the  eye 
backwards,  we  meet  with  considerable  resistance ;  the  movements  of  the 
eye  are  limited,  therefore,  to  its  rotations. 

These  rotations  are  made,  at  least  approximately,  around  a  center 
which,  according  to  the  determinations  of  Bonders,  is  situated  about 
10  mm.  in  front  of  the  posterior  surface  of  the  sclera,  or  14  mm.  behind 
the  summit  of  the  cornea.  It  coincides  with  the  center  of  the  posterior 
surface  of  the  globe,  supposed  to  be  spherical.  It  is  not  certain  that  the 
center  of  rotation  is  exactly  the  same  for  movements  in  different  di- 
rections. 

Danders,  in  collaboration  with  Dojer,  determined  the  position  of  the 
center  of  rotation  of  the  eye  in  the  following  manner.  He  first  measured 
the  diameter  of  the  cornea  with  the  ophthalmometer  of  Helmholts,  and 
then  placed  a  hair  (a,  fig.  175)  stretched  vertically  in  a  ring,  in  front  of 
the  middle  of  the  cornea.  He  then  examined  the  angular  size  of  the 

287 


2SS 


PHYSIOLOGIC  OPTICS 


lateral  movements  of  the  look,  which  the  observed  person  had  to  make, 
in  order  that  the  hair  would  be  seen  successively  in  coincidence  with  the 
left  and  right  borders  of  the  cornea.  Let  ACD  (fig.  175)  be  one  of  these 
movements,  p  half  the  diameter  of  the  cornea,  and  x  the  distance  CE. 
Then  we  have  p  =  xtg  ACD,  from  which  we  can  calculate  x.  Adding  to 


Fig.  175. 

this  distance  the  height  of  the  cornea,  we  find  the  distance  of  the  center 
of  rotation  from  the  cornea. 


Fig.  176. 

The  six  motor  muscles  form,  as  we  know,  three  pairs,  (i)  which  cause 
the  eye  to  turn  around  three  axes  passing  through  the  center  of  rota- 

(1)  [This  statement  is  only  approximately  true,  as  according  to  the  careful  measurements  of  Volk- 
mann,  each  of  the  six  muscles  of  the  eye  seems  to  rotate  the  latter  around  its  own  axis.  See  paper  by 
the  translator  in  the  Archives  of  Ophthalmology,  Vol.  XXVII,  No.  1, 1898 :  Are  our  present  ideas  about 
the  mechanism  of  the  eye-movements  correct?]— W. 


THE  LAW  OF  LltiTINtt  289 

tion  of  the  eye.  The  axis  of  the  external  and  internal  recti  is  vertical. 
The  axes  of  the  two  other  pairs  are  situated  in  the  horizontal  plane. 
The  nasal  extremity  of  the  axis  of  the  superior  and  inferior  recti,  BA 
(fig.  176)  is  situated  a  little  in  front,  so  as  to  form  an  angle  of  about  70° 
with  the  visual  line.  The  temporal  extremity  of  the  axis  of  the  oblique 
muscles  CD  (fig.  176)  is  directed  very  much  forwards;  it  forms  an  angle 
of  about  35°  with  the  visual  line. 

The  internal  and  external  recti  turn  the  eye,  therefore,  directly  in- 
wards and  outwards.  The  superior  and  inferior  recti  direct  the  look 
upwards  and  downwards,  but  at  the  same  time  a  little  inwards.  The 
inferior  and  superior  oblique  direct  the  look  either  downwards  or  up- 
wards but  at  the  same  time  outwards.  The  look  is  directed  straight 
upwards  by  the  combined  action  of  the  superior  rectus  and  the  inferior 
oblique,  and  the  direction  downwards  is  obtained  by  the  combined  action 
of  the  inferior  rectus  and  superior  oblique. 

The  muscles  make  possible  the  rotation  of  the  globe  around  any  axis. 
This  is  all  that  it  is  of  importance  to  know  for  the  physiology  of  the 
eye.  We  must  not  think  that  the  eye  turns  oftener  around  the  axes 
which  we  have  just  described,  than  around  the  intermediary  axes.  It 
seems,  indeed,  that  all  six  muscles  are  concerned  each  time  the  eye 
makes  any  motion;  the  axis  around  which  the  eye  turns  is,  therefore, 
always  different  from  the  three  which  we  have  just  mentioned. 

117.  The  Law  of  Listing.  —  Supposing  the  head  to  be  motionless,  the 
position  of  the  eye  is  determined  for  a  given  point  of  fixation.  This 
is  far  from  being  evident  a  priori,  for  the  eye  could  still  perform  rota- 
tions around  the  visual  line.  Each  time  that  the  look  returns  to  the  same 
point,  no  matter  in  what  way,  the  eye  always  reassumes  the  same  posi- 
tion (Bonders).  If,  by  fixing  a  colored  ribbon  stretched  horizontally,  we 
produce  an  after  image,  and  then  project  the  latter  on  a  wall,  keeping 
the  head  motionless,  the  image  assumes  a  position  which  is  not  always 
horizontal,  but  which  is  always  the  same  every  time  that  the  look  returns 
to  a  given  point.  This  position  is  determined  by  the  law  of  Listing. 

There  exists  a  certain  direction  of  the  visual  line  in  relation  to  the 
head,  which  we  call  primary  direction;  the  corresponding  position  of  the 
eye  is  named  primary  position,  and  every  other  position  (direction)  is 
called  secondary.  The  primary  direction  generally  corresponds  to  the 
direction  which  the  visual  line  assumes  when  we  look  at  the  horizon, 
giving  to  the  head  the  position  which  seems  most  natural ;  but  it  happens 
quite  frequently,  however,  that  one  is,  under  these  circumstances, 


290 


PHYSIOLOGIC   OPTICS 


obliged  to  lower  the  look  slightly,  in  order  to  put  the  eye  in  the 
primary  position.  In  this  case,  one  is  obliged  to  lean  the  head  slightly 
backwards  in  order  to  make  the  primary  direction  horizontal.  We  must 
suppose  this  direction  invariably  connected  with  the  head,  in  all  the 
movements  of  which  it  partakes. 

According  to  the  law  of  Listing,  the  eye  may  be  brought  from  the  primary 
position  to  any  secondary  position  by  a  rotation  around  an  axis  perpendicular 
to  the  two  successive  directions  of  the  visual  line.  This  defines  for  us  at  the 
same  time  the  primary  position.  —  The  axes  of  Listing  are  all  contained 
in  a  plane  perpendicular  to  the  primary  direction  and  pass  through  the 
center  of  rotation  of  the  eye.  This  plane  is,  therefore,  as  invariably, 
connected  with  a  head. 

To  demonstrate  the  law  of  Listing,  we  place  ourselves  at  a  distance 
of  one  or  two  meters  from  a  wall  on  which  is  placed  a  fixation  mark  A 
(fig.  177),  on  a  level  with  the  eyes.  It  is  necessary  to  make  the  position  of 
the  head  secure.  If  we  do  not  wish  to  make  verv  exact  measurements, 


Fig.  177. 

a  head-rest,  like  that  of  the  ophthalmometer  of  Javal  and  Schioetz,  suf- 
fices. If,  on  the  contrary,  we  desire  a  very  great  exactness,  we  use  the 
little  mouth-board  (planchette)  of  Helmholtz,  the  border  of  which  is  cov- 
ered with  sealing  wax.  We  squeeze  the  planchette  between  the  teeth 
while  the  sealing  wax  is  still  warm,  so  that  the  latter  may  receive  the 
imprint  of  the  teeth.  We  then  fix  the  planchette  on  a  stand,  so  as  to 


THE  LAW   OF  LISTING 


291 


be  able  to  turn  it  to  the  right  or  to  the  left  or  to  incline  it  any  number 
of  degrees  fixed  upon  (Hering). 

We  place  on  the  wall,  at  A,  a  rectangular  cross  so  that  its  arms  may 
be  horizontal  and  vertical.  The  cross  ought  to  contrast  boldly  with  the 
background,  so  as  to  permit  us  to  obtain  a  very  pronounced  after  image 
by  fixing  it  for  a  little  while.  We  take  the  planchette  between  the  teeth 
and,  inclining  the  head  (with  the  planchette)  a  little  forward  or  back- 
ward, or  inclining  it  a  little  to  the  right  or  to  the  left,  we  find  a  position 
such  that  on  moving  the  look  along  the  prolongation  of  each  of  the 
arms  of  the  cross,  the  after  image  of  this  arm  glides  all  the  time  on 
itself  (fig.  177).  We  then  observe  that  there  exists  only  one  position 
of  the  .head  for  which  this  is  possible;  for  every  other  position  of 
the  head  the  after  image  of  the  cross  turns  around  during  the  dis- 
placement of  the  look.  When  we  have  found  this  position  of  the  head, 
we  fix  the  planchette,  so  as  to  be  able  to  again  find  the  position  every 
time  that  we  take  the  planchette  between  the  teeth.  Then,  when  we  fix 
the  point  A,  the  eye  is  in  the  primary  position.  Suppose,  indeed,  that 

XXX 


x --) 


c X 


X      X      "X 

Fig.  178. 

we  fix  a  second  point  B,  situated  on  a  prolongation  of  the  horizontal 
arm:  since  the  meridian  which  was  horizontal  when  fixing  A,  is  also 
horizontal  when  fixing  B,  it  is  clear  that  the  look  may  be  brought  from 
A  to  B  by  a  motion  around  a  vertical  axis,  that  is  to  say,  around  an  axis 
perpendicular  to  the  two  directions  of  the  visual  line.  It  is  the  same  for 
displacement  in  the  vertical  direction.  In  order  to  demonstrate  that 
this  is  also  the  case  for  the  oblique  displacements,  we  tilt  the  cross  (fig. 


202 


PHYSIOLOGIC   OPTICS 


178).  It  is  then  easy  to  prove  that  the  after  image  of  one  of  the  arms 
of  the  cross  glides  all  the  time  on  its  prolongation,  when  the  look  follows 
this  prolongation,  and  that,  consequently,  the  eye  turns  around  an  axis 
perpendicular  to  this  meridian.  The  law  of  Listing  is  thus  verified. 

If,  in  these  experiments,  the  look  does  not  follow  the  prolongation  of 
one  of  the  arms  of  the  cross,  we  observe  phenomena  which  might  seem 
in  contradiction  with  the  law  of  Listing.  Thus  fixing  the  point  C  (fig. 
177)  we  observe  that  the  after  image  of  the  vertical  arm  of  the  cross  is 
no  longer  vertical ;  it  has  undergone  a  rotation,  and  the  upper  extremity 
is  carried  to  the  right.  A  little  reflection  shows  that  this  is  simply  a  con- 
sequence of  the  law  of  Listing,  and  that  the  meridian  which  was  vertical 
when  fixing  A,  cannot  remain  vertical  when  the  eye  turns  around  an 
axis  perpendicular  to  the  direction  AC.  Bonders,  who  first  described 
this  phenomenon,  attributed  it  to  a  rotary  movement  (Raddrehung)  of 
the  eye,  that  is  to  say,  a  rotation  around  the  visual  line,  but  it  is  clear 
that  such  a  rotation  cannot  take  place  since  the  axis  of  Listing  is  per- 


Fig.  179. 

pendicular  to  the  visual  line.  —  The  horizontal  arm  of  the  cross  seems 
to  have  suffered  a  rotation  in  a  contrary  direction,  but  this  is  merely 
the  result  of  the  projection  of  the  after  image  on  a  plane  which  is  not 
perpendicular  to  the  visual  line,  (i)  If  we  project  the  image  on  the  con- 

(1)  [How  much  these  after  images  ought  to  be  inclined  towards  the  horizontal  and  vertical  lines  of 
the  wall  has  been  explained  by  the  translator  in  a  paper  entitled  "The  Law  of  Listing  and  Some  Dis- 
puted Points  about  Its  Proof."  Archives  of  Ophthalmology,  Vol.  XXVIII,  March,  1899.  The  relation 
between  these  angles  and  the  angles  of  Helmholtz  is  elucidated  in  a  paper  by  Dr.  O.  Hay  in  the  Journal 
of  the  Boston  Society  of  Medical  Sciences,  in  Oct.,  1899,  and  in  a  paper  by  Professor  L.  Hermann,  in 
Pfliiger's  Archiv  der  Physiologic,  Nov.,  1899.]  —  W. 


THE  LAW  OF  LISTING  293 

cave  surface  of  a  hollow  hemisphere,  in  the  center  of  which  is  the  eye, 
the  cross  remains  rectangular  and  seems  to  have  suffered  a  complete 
rotation  to  the  right  (fig.  179).  —  In  these  experiments,  the  position  of 
the  two  eyes  is  exactly  the  same:  we  can  cover  sometimes  one  eye, 
sometimes  the  other,  and  the  position  of  the  after  image  does  not 
change. 

It  must  be  noted  that  the  eye  may  be  transferred  from  the  primary 
position  to  a  secondary  position,  by  rotating  around  the  axis  of  Listing. 
I  do  not  say  that  it  really  makes  this  movement,  for  the  law  of  Listing 
defines  solely  the  position  of  the  eye  in  the  state  of  repose.  —  We  know 
nothing,  or  almost  nothing,  of  the  manner  in  which  the  eye  makes  its 
movements.  There  is  no  reason  to  assert  that  it  turns  around  the  axes 
of  Listing,  nor  even  to  suppose  that  the  look  always  follows  the  same 
way  to  go  from  one  point  to  another.  The  best  method  of  studying  this 
question  would  probably  be  to  bring  the  look  quickly  from  one  point 
to  another,  leaving  the  eye  exposed  to  a  pretty  intense  light.  The  after 
image  of  the  luminous  source  then  assumes  the  form  of  a  line  which 
permits  some  conclusion  as  to  the  nature  of  the  movement. 

What  we  have  said  suffices  to  determine  any  position  of  the  eye.  If 
the  look  passes  from  one  secondary  direction  to  another,  the  position 
of  the  eye  is  nevertheless  determined  by  the  law  of  Listing,  since,  having 
reached  its  new  secondary  position,  it  must  have  the  same  position  as 
if  it  had  reached  there,  starting  from  the  primary  position.  Note  that 
the  look  cannot  be  brought  from  one  secondary  position  to  another  by 
turning  around  an  axis  perpendicular  to  the  two  directions  in  the  visual 
line.  For,  if  the  look  goes  from  B  to  C  (fig.  177),  following  the  pro- 
longation of  the  vertical  arm,  we  observe  that  the  after  image  of  this 
arm  starts  from  the  prolongation  and  rotates  more  and  more  so  as  to 
attain  the  position  which  it  should  have  when  the  look  will  have  arrived 
at  C.  In  making  this  movement  of  the  look,  the  eye  does  not  rotate, 
therefore,  around  an  axis  perpendicular  to  the  visual  line,  and  we  can  in 
this  case  speak  of  a  true  rotary  movement.  If  we  displace  the  look  so 
that  the  after  image  moves  always  on  itself,  the  point  of  fixation  de- 
scribes a  curve  the  convexity  of  which  is  turned  towards  the  point  A. 
It  is  the  same  for  the  horizontal  arm :  if  we  bring  the  look  from  C  to  E, 
so  that  its  after  image  moves  on  itself,  we  obtain  a  curve  with  its  con- 
vexity downwards.  The  following  illusion,  described  by  Hclmholts,  re- 
sults from  this  fact. 

If,  after  having  fixed  the  point  A  in  the  primary  position,  we  raise 
the  eyes  and  survey  quickly  with  the  look  a  horizontal  straight  line 


294  PHYSIOLOGIC   OPTICS 

situated  higher  up,  it  appears  concave  towards  the  floor  (compare  page 
217).  This  is  due  to  the  fact  that  oblique  directions  of  the  look  are 
very  rare.  Generally,  we  take  care  when  we  desire  to  look  at  any  object, 
to  turn  the  head  in  such  a  way  that  the  eyes  are  nearly  in  their  primary 
position,  and  that  the  horizontal  lines  are  drawn  on  the  retinal  horizon 
(the  meridian  of  the  retina  which  is  horizontal  in  the  primary  position: 
in  the  experiment  fig.  177,  the  retinal  horizon  is  marked  by  the  after 
image  of  the  horizontal  arm  of  the  cross).  On  account  of  this  custom 
we  have  a  tendency  to  consider  the  direction  of  the  retinal  horizon  as 
horizontal,  even  when  it  is  not.  Looking  upwards  and  to  the  left,  the 
retinal  horizon  inclines  its  right  extremity  downwards,  and,  if  we  con- 
sider this  direction  as  horizontal,  it  follows  that  the  straight  line  which 
we  observe  must  appear  inclined  to  the  left;  when  the  look  reaches  the 
other  extremity,  this  latter  will  seem  inclined  to  the  right;  thus  it  is 
that  the  line  assumes  its  curved  aspect,  but  we  must  survey  it  quickly, 
otherwise  it  seems  rather  to  lean  sometimes  to  the  right,  sometimes  to 
the  left. 

ANOTHER  METHOD  OF  DEMONSTRATING  THE  LAW  OF  LISTING.  —  As 
the  retinal  horizon  passes  through  the  papilla,  we  can  use  the  position  of 
the  spot  of  Mariotte  to  account  for  its  direction.  Pick  drew,  on  a  card- 
board movable  around  a  point  O,  a  black  spot  just  large  enough  to  dis- 
appear in  the  spot  of  Mariotte,  when  he  fixed  the  point  O  in  the  primary 
position.  Turning  the  head  to  the  right  or  to  the  left  and  inclining  it  at 
the  same  time,  while  he  continued  to  fix  the  point  O,  the  spot  reappeared 
and  he  then  measured  how  much  it  was  necessary  to  turn  the  cardboard 
to  make  it  disappear  again.  —  Proceeding  thus,  we  find,  as  by  the  pre- 
ceding method,  that  the  eyes  follow  pretty  exactly  the  law  of  Listing,  at 
least  while  the  visual  lines  remain  parallel. 

118.  Experiments  of  Meissner.  —  Apparently  vertical  meridian.  — 
There  exists  another  method  which  has  been  described  by  Meissner, 
and  which  enables  us  to  verify  the  law  of  Listing  in  a  very  exact  manner. 
But  before  explaining  this  method,  I  must  mention  a  singular  phenom- 
enon which  we  meet  when  we  wish  to  judge  whether  a  line  is  vertical 
or  not. 

We  hold  a  plumb-line  in  front  of  a  wall  painted  uniformly  and  we  fix 
a  point  situated  a  little  in  front  of  this  line  (i) :  we  then  see  the  latter 
in  double  homonymous  images,  and  we  would  expect  to  see  two  vertical 


(1)  We  must  not  place  ourselves  too  near  the  line,  in  order  that  the  influence  of  convergence,  of 
which  I  shall  speak  immediately,  may  not  interfere. 


TEE  LAW  OF  LISTING  295 

and  parallel  lines;  but  the  two  lines  seem  to  converge  upwards:  seen 
with  the  right  eye,  the  upper  extremity  of  the  line  seems  to  lean  to 
the  left.  If  we  fix  a  point  situated  behind  the  line,  the  images  are 
crossed  and  seem  to  converge  downwards.  A  vertical  line  seen  with 
one  eye  only  does  not,  therefore,  appear  vertical,  but  its  upper  extremity 
seems  to  lean  to  the  left  or  to  the  right,  according  as  it  is  the  right  eye 
or  the  left  eye  which  looks  at  it.  —  Looking  at  a  rectangular  cross,  one 
of  the  arms  of  which  is  horizontal  and  the  other  vertical,  the  two  angles, 
the  upper  right  and  lower  left,  will  appear,  for  the  right  eye,  larger  than 
the  other  two,  while  the  contrary  takes  place  for  the  left  eye. 

Since,  for  the  right  eye,  a  vertical  line  appears  to  lean  to  the  left,  there 
must  exist  a  line  leaning  to  the  right,  which  seems  vertical.  We  can 
determine  the  direction  of  this  line  by  observing  a  white  disc  movable 
around  its  center  and  on  which  we  draw  one  diameter.  Along  the 
border  is  a  scale  graduated  in  degrees,  the  zero  of  which  corresponds 
to  the  vertical  line,  and  which  must  be  placed  so  as  not  to  be  visible. 
The  observer  tries  to  turn  the  disc  so  as  to  place  the  diameter  vertically. 
With  the  right  eye  he  places  nearly  always  the  upper  extremity  some 
degrees  too  far  to  the  right,  with  the  left  eye  some  degrees  too  far  to 
the  left.  For  the  horizontal  meridian,  the  phenomenon  is  less  pro- 
nounced. —  It  is  necessary  to  arrange  the  experiment  in  such  a  manner 
that  the  observer  cannot  be  guided  by  the  view  of  the  surrounding 
objects. 

Another  method  of  determining  the  angle  between  the  apparently 
vertical  meridians  of  the  two  eyes  has  been  described  by  Volkmann  (fig. 
1 80).  He  placed  two  small  revolving  discs  on  a  vertical  wall  so  that 
the  distance  separating  their  centers  would  be  equal  to  the  distance 
between  the  eyes.  On  each  disc  was  shown  one  radius.  He  observed 
the  discs  as  with  the  stereoscope,  the  right  eye  fixing  the  disc  on 


Fig.   180.  —  Discs  of  Volhnann. 

the  right,  the  left  eye  that  on  the  left.    He  placed  one  of  the  radii  ver- 
tically, and  then  tried  to  place  the  other  so  that  the  two  radii  would 


29G 


PHYSIOLOGIC  OPTICS 


appear  to  form  a  single  straight  line ;  it  was  necessary  that  they  should 
form  an  angle  of  about  two  degrees.  —  Among  the  stereoscopic  tests 
which  are  given  in  Javal's  manual  on  strabismus,  several  show  small 
discs  like  those  of  Volkmann,  on  which  the  two  radii  are  exactly  parallel. 
On  overlapping  the  two  discs  they  form  only  one,  but  the  diameter 
appears  broken;  the  two  radii  seem  to  form  an  obtuse  angle.  If  we  pre- 
sent to  the  right  eye  the  figure  which  was  intended  for  the  left  eye,  the 
angle  seems  turned  in  the  opposite  direction. 

It  is  probable  that  these  phenomena  are  due  to  the  more  important 
part  played  by  the  downward  look  in  everyday  life :  we  look  downwards 
when  reading,  and  when  walking  the  look  most  frequently  follows  the 
ground,  etc.  By  repeating  the  experiment  of  Meissner,  we  will  find  that 
the  two  images  appear  parallel  if  we  bring  the  lower  extremity  of  the 
plumb-line  towards  the  observer,  until,  in  relation  to  the  line  of  the  look, 
it  has  almost  the  inclination  which  a  book  has  when  we  hold  it  in  the 
ordinary  position  of  reading.  If  we  draw  a  straight  line  on  a  sheet  of 
paper  placed  on  a  table  so  that  this  line  is  in  the  median  plane  of  the 
observer,  we  see,  on  placing  ourselves  in  the  position  which  we  ordi- 
narily assume  in  order  to  read  or  write,  making  the  visual  lines  parallel, 
that  the  two  images  of  the  line  appear  parallel.  Glancing  at  figure  181, 
in  which  the  eyes  are  shown  projected  on  the  table,  it  is  easy  to  see  that 
the  extremity  A  of  the  line  which  is  nearest  the 
observer  forms  its  image  on  more  peripheral 
parts  of  the  retina  than  the  extremity  B.  The 
two  meridians  of  the  retinge  which  receive  the 
images,  converge  therefore  downwards,  since  the 
extremity  A  forms  its  image  higher  and  more 
towards  the  periphery  than  the  extremity  B. 
We  have  formed  our  judgment  according  to  this 
experiment,  and  when,  under  other  circum- 
stances, a  line  comes  to  form  its  image  upon 
this  meridian,  we  consider  it  as  situated  in  the 
median  plane.  According  to  Javal,  the  experi- 
ments establishing  binocular  vision  in  persons 
affected  with  strabismus,  confirm  absolutely  the 
preceding  explanations. 
Fig.  181.  One  can  understand  how  these  methods  may 

be  used,  if  not  to  directly  verify  the  law  of  Listing,  at  least  to  compare 
the  position  of  the  two  eyes.  Working  in  the  primary  position,  and  with 
the  two  visual  lines  parallel,  Volkmann  found  that  it  was  necessary  to 


THE  LAW  OF  LISTING  297 

give  to  the  radii  of  his  discs  directions  converging  about  two  degrees 
downwards,  in  order  that  they  would  appear  to  form  an  unbroken  line. 
Leaving  the  visual  lines  parallel,  he  found  the  same  angle  for  all  sec- 
ondary directions,  and  the  law  of  Listing  was  thus  verified.  It  is  other- 
wise when  we  converge.  After  having  placed  the  eyes  in  the  primary 
position,  Volkmann  converged  for  a  point  situated  at  30  cm.  in  the  same 
horizontal  plane.  Since,  under  these  circumstances,  the  eyes  pass  from 
the  primary  position  to  an  internal  position,  the  law  of  Listing  would 
have  demanded  that  the  directions  of  the  two  radii  would  continue  to 
form  an  angle  of  two  degrees ;  but  Volkmann  found  that  it  was  necessary 
to  increase  their  inclination  to  four  degrees,  in  order  that  the  resulting 
line  would  be  seen  unbroken.  Converging,  each  eye  had,  therefore, 
made  a  rotary  movement  of  one  degree,  which  it  would  not  have  made 
by  taking  the  same  position,  if  the  visual  lines  were  parallel.  The  eyes 
do  not,  therefore,  follow  exactly  the  law  of  Listing  when  the  visual  lines 
are  not  parallel. 

The  following  experiment  is  very  easy  to  perform.  We  place  two 
candles,  one  meter  from  each  other,  and  we  observe  them  at  one  or  two 
meters  distance,  taking  care  to  put  the  eye  nearly  in  the  primary  posi- 
tion. We  then  try  to  converge  as  if  to  fuse  the  two  candles.  We  will 
then  observe  that  they  appear  slightly  inclined  towards  each  other ;  the 
nearer  to  each  other  we  bring  the  candles,  the  greater  the  inclination ; 
the  angle  between  the  two  candles  may  reach  15°  or  more.  The  image 
of  the  left  eye  is  inclined,  the  upper  extremity  to  the  right  and  vice  versa. 
Bering,  and  later  Landolt,  have  made  exact  measurements  of  these  devia- 
tions from  the  law  of  Listing. 

119.  Historical.  —  The  question  of  knowing  whether  the  eye  per- 
forms rotary  movements  around  the  visual  line  has  been  much  disputed. 
Hneck  thought  that  he  observed  that  the  eye  undergoes  a  rotation  in  a 
reverse  direction  when  the  head  is  leant  towards  the  shoulder  so  that 
the  meridian  of  the  retina,  which  is  vertical  in  the  ordinary  circumstances 
of  life,  remains  vertical.  He  attributed  this  rotation  to  the  contraction 
of  the  oblique  muscles,  and  his  ideas  were  shared  by  all  scientists  until 
Ruete  demonstrated  the  error  of  Hneck  by  means  of  the  examination  with 
the  after  images,  and  gave  a  correct  explanation  of  the  action  of  the 
oblique  muscles.  Bonders  took  up  the  question,  and  enunciated  a  law 
which  bears  his  name,  according  to  which  the  position  of  the  after  image 
is  always  the  same  for  the  same  direction  of  the  eye ;  but  the  question 
was  stated  clearly  only  by  the  enunciation  of  the  law  of  Listing,  which 


20S  PHYSIOLOGIC   OPTICS 

is  found  for  the  first  time  in  the  treatise  of  Ruete  of  1853.  Listing  did 
not  publish  it  himself.  Meissner  was  the  first  who  verified  this  law  by 
experiments. 

After  the  experiments  of  Ruete  and  Bonders  everybody  supposed  the 
rotary  movements  of  Hueck  did  not  exist,  when  Javal  demonstrated  that 
the  eye  performs,  nevertheless,  a  very  slight  rotation  in  this  direction. 
He  had  observed,  indeed,  that  when  he  leant  his  head  to  the  right  or  to 
the  left  the  direction  of  the  axis  of  his  cylindrical  glasses  no  longer  coin- 
cided with  that  of  his  astigmatism.  This  is,  perhaps,  the  most  exact 
test  to  see  whether  glasses  are  properly  placed.  Helmholtz  verified  the 
fact  by  placing  on  a  level  with  his  eyes  a  small  colored  band  on  a  frame 
fixed  on  his  planchette.  By  leaning  the  head  with  the  planchette,  the 
secondary  image  turned  a  little  in  the  opposite  direction,  so  as  no  longer 
to  coincide  with  the  ribbon. 

Bibliography.  —  GEnvres  de  Young,  edited  by  Tscherning,  p.  145.  —  Hueck.  Die  Ach- 
sendrehung  des  Auyes.  Dorpat,  1838.  —  Donders  (F.  C.).  Hollandische  Beitrage,  1848.  — 
Ruete.  Lehrbuch  der  Ophthalmologie,  1853.  —  Fick  (A.).  Die  Bewegungen  des  menschlichen 
Augapfels.  Zeitschrift  fur  rat.  Medizin,  IV,  1854.  —  Meissner  (G.).  Die  Bewegungen  des 
Auges.  Arch.  f.  Ophth.,  II,  1,  1855.  — v.  Helmholtz.  Ueber  die  normalen  Bewegungen  des 
menschlichen  Auges.  Arch.f.  Ophth.,  IX,  2,  1863.  —  Volkraann  (A.  W.).  Physiologische  Un- 
ersuchungen  im  Gebiete  der  Optik.  II.  Leipzig,  1864.  —  Donders  and  Doyer  in  Donders. 
Anomalies  of  the  Refraction  of  the  Eye.  London,  1864,  p.  180.  —  Javal  (E.).  in  de  Wecker. 
Traite  des  maladies  des  yeux.  I,  p.  815.  Paris,  1866.  —  Tscherning  (M.).  La  loi  de  Listing. 
Paris,  1887. 


CHAPTER    XX. 

THE  OCULAR  MOVEMENTS. 

120.  Jerking  Movements  of  the  Eyes.  —  It  seems  as  if  the  eye  should 
foe  kept  motionless  in  order  to  obtain  an  impression,  at  least  an  impres- 
sion which  can  be  perceived  with  some  distinctness.     If,  in  a  railroad 
train  which  is  going  quite  fast,  we  fix  a  point  on  the  window,  the  land- 
scape appears  confused,  the  images  of  its  different  parts  succeeding  one 
another  too  quickly  on  the  retinae  to  be  perceived  distinctly.    Observ- 
ing the  eyes  of  any  one  who  is  looking  at  the  landscape,  we  see  that 
-they  move  by  jerks.    The  eyes  of  the  person  observed  make  alternately 
a  rapid  movement  in  the  direction  of  the  train  to  catch  the  object,  and 
a  slower  movement  in  the  opposite  direction  to  keep  the  image  of  the 
object  on  the  fovca.    Then  they  again  make  a  rapid  movement  with  the 
train  to  catch  a  new  object,  and  so  forth. 

The  eye  cannot  fix  the  same  point  for  even  a  little  while,  without  the 
formation  of  after  images  which  annoy  the  vision,  and  without  the  phe- 
nomenon of  Troxler  interfering.  The  eyes  are,  therefore,  in  perpetual 
motion  which  is  made  by  jerks:  they  fix  a  point,  make  a  movement,  fix 
another  point,  and  so  forth.  While  reading,  the  eyes  move  also  by  jerks, 
four  or  five  for  each  line  of  an  ordinary  book.  Lamare  constructed  a 
small  instrument,  formed  by  a  point  which  is  supported  on  the  eye 
across  the  upper  eyelid,  and  which  is  fastened  to  the  ears  of  the  observer 
by  rubber  tubes.  With  this  instrument  each  movement  of  the  eye  causes 
a  sound  to  be  heard.  We  hear  four  or  five  slight  sounds  during  the 
reading  of  one  line,  and  a  louder  sound  when  we  begin  to  read  a  new 
line. 

121.  Relative  Movements  of  the  two  Eyes.  —  The  relative  movements 
of  the  two  eyes  are  governed  by  the  necessity  of  seeing  the  object  single. 
It  is  necessary  for  this  purpose  that  an  image  of  the  object  fixed  be 
formed  on  each  fovea.     When,  after  having  looked  at  an  object  at  a 
certain  distance,  we  look  at  another  situated  at  the  same  distance,  the 

299 


300  PHYSIOLOGIC   OPTICS 

two  eyes  make  associated  movements :  both  turn  to  the  right,  or  both 
to  the  left,  upwards  or  downwards,  etc.,  and  one  as  much  as  the  other. 
If  the  objects  are  both  in  the  median  plane,  but  at  different  distances, 
it  is  necessary,  in  order  to  bring  the  look  from  the  more  distant  to  the 
nearer,  that  the  eyes  make  a  movement  of  convergence:  both  turn  in- 
wards to  the  same  extent;  finally,  if  the  two  objects  are  in  different 
directions,  the  second  nearer  than  the  first,  the  eyes  perform  a  com- 
bination of  an  associated  movement  and  a  movement  of  convergence.  — 
If  the  second  object  is  situated  farther  away  than  the  first,  the  eyes 
make  a  movement  of  divergence  (negative  convergence). 

It  is  impossible  to  cause  a  movement  to  be  made  with  one  eye  without 
the  other  moving  also,  or  at  least  without  its  having  a  tendency  to  move. 
A  very  simple  experiment  would  seem  to  indicate  the  contrary.  Sup- 
pose that  the  two  eyes  fix  a  point  a,  and  that  we  place  in  the  visual  line 
of  the  right  eye  an  object  b.  If  we  ask  the  observed  person  to  fix  b,  the 
left  eye  is  directed  towards  this  point,  while  the  right  eye  remains  mo- 
tionless. But,  if  we  observe  closely,  we  shall  see  that  this  eye  makes 
really  two  slight  changes  of  position,  for  instead  of  receiving  no  innerva- 
tion,  as  one  would  think,  its  muscles  receive  two,  one  which  would 
cause  it  to  make  an  associated  movement  (to  the  right),  and  another 
which  would  cause  it  to  make  a  movement  of  convergence  (to  the  left) ; 
the  results  of  these  two  innervations  neutralize  so  that  the  eye  remains 
motionless.  It  was  Hcring  who  described  this  experiment,  which  is  of 
great  importance  for  the  understanding  of  the  relation  between  the 
movements  of  the  two  eyes. 

The  two  kinds  of  movements  of  which  we  have  spoken  are  the  only 
ones  which  the  eyes  have  usually  to  make  in  the  interest  of  fusion,  and 
they  are  the  only  ones  which  they  can  make.  It  is  possible,  however, 
to  make  them  diverge  a  little.  —  I  mean  absolute  divergence  and  not 
relative  divergence,  which  is  only  a  less  degree  of  convergence.  —  We 
can  make  this  divergence  necessary  for  fusion  by  placing  before  one  eye 
a  prism  with  its  apex  turned  outwards ;  but  the  angle  of  the  prism  which 
the  eyes  can  thus  overcome  does  not  much  exceed  five  degrees.  We 
are  unable  to  raise  the  look  of  one  eye  while  leaving  the  other  motion- 
less ;  but  by  placing  before  one  eye  a  very  weak  prism,  apex  upwards, 
this  eye  deviates  a  little,  however,  in  the  interest  of  fusion.  The  prism 
which  we  may  thus  overcome  generally  does  not  exceed  two  or  three 
degrees. 

These  peculiarities  of  the  ocular  movements  are  evidently  not  due  to 
the  muscular  apparatus.  There  is,  indeed,  nothing  to  prevent  the  right 


THE   OCULAR  MOVEMENTS  301 

eye  from  making  a  movement  to  the  right,  but  it  cannot  make  it  while 
the  left  eye  makes  a  movement  to  the  left.  If  we  cannot  perform  two 
movements  at  once,  this  is  due  to  the  fact  that  we  cannot  give  the  neces- 
sary innervation  for  this  movement.  And  we  cannot  give  this  innerva- 
tion  because  we  are  not  accustomed  to  give  it,  since,  far  from  being 
useful,  it  would  be  harmful,  on  account  of  the  diplopia  to  which  it  would 
necessarily  give  rise.  —  The  impulse  which  guides  the  ocular  movements 
is,  up  to  a  certain  point,  analogous  to  that  which  makes  us  keep  our 
eyes  open  and  the  head  erect,  with  this  difference,  however,  that  the  in- 
nervation which  guides  the  movement  of  the  eyes  is  much  more  rigor- 
ous ;  we  can  lower  the  head  or  close  the  eyes  if  we  desire  to  do  so,  but 
we  cannot  put  the  eyes  in  divergence.  The  innervation  in  question  dis- 
appears during  sleep.  When  struggling  against  sleep,  we  observe 
diplopia,  and  the  two  images  affect  relative  positions  which  they  never 
have  in  a  state  of  wakefulness.  The  homonymous  images  which  we 
obtain  by  squinting  voluntarily  are  always  parallel,  if  I  except  the  phe- 
nomena mentioned  in  the  preceding  chapter,  and  they  are  at  the  same 
height  (if  the  head  be  kept  erect).  The  images  which  we  obtain  when 
sleep  comes  upon  us  have,  on  the  contrary,  wholly  irregular  positions : 
sometimes  one  is  higher  than  the  other,  sometimes  they  undergo  rota- 
tions, etc.  At  the  same  time  the  eyelids  have  a  tendency  to  close  and 
the  head  to  fall. 


122.  Measurement  of  Convergence.  -  -  This  measurement  is  made  pre- 
ferably with  the  rotary  prism  of  Cretes.  As  we  know,  this  instru- 
ment is  composed  of  two  superimposed  prisms  of  the  same  strength.  A 
special  mechanism  allows  them  to  be  turned  in  opposite  directions. 
When  the  apices  have  the  same  direction,  the  effect  is  double  that  of 
each  of  the  prisms.'  If  we  cause  them  to  rotate  the  deviation  always 
takes  place  in  the  same  direction,  but  it  gradually  diminishes  and  dis- 
appears when  the  apices  are  directed  in  different  directions.  The  instru- 
ment replaces,  therefore,  a  whole  series  of  prisms  of  different  strength. 

We  place  the  prism  with  the  apex  outwards  while  the  patient  looks 
at  a  distant  flame,  and  we  increase  the  strength  of  the  prism  until  the 
subject  sees  two  images  of  the  flame.  We  thus  find  abduction;  for 
healthy  eyes,  it  is  five  to  seven  degrees  of  prism.  We  then  turn  the  prism 
apex  inwards  and  increase  its  strength  until  diplopia  is  produced.  Adduc- 
tion is  much  stronger  than  abduction ;  it  may  reach  20  or  30  degrees  of 
prism,  or  more.  We  can  also  measure  adduction  and  abduction  for  a 
nearer  point.  Adduction  often  exceeds  the  maximum  value  of  the  prism 


302 


PHYSIOLOGIC   OPTICS 


of  Cretes,  and  on  the  other  hand,  it  quite  frequently  happens  that  it  is- 
greater  than  we  find  it  at  that  moment,  because  the  observed  person: 
does  not  do  his  best  to  fuse  the  images.  It  would  also  be  better  to 
measure  the  adduction  simply  by  trying  how  near  we  could  approach 
an  object  without  its  appearing  double  (ophthalmodynamometer  of 
Landolt).  —  We  sometimes  meet  rare  cases  of  defect  of  convergence, 
where  the  adduction  is  greatly  diminished,  while  the  abduction  is  normal. 
—  In  other  cases  both  are  diminished:  the  patient  can  fuse  well  two- 
images  which  are  formed  on  the  two  maculae,  but  he  experiences  no 
need  of  fusion;  even  when  the  double  images  are  very  near  each  other,, 
the  eyes  do  not  make  the  slight  motion  necessary  to  fuse  them. 

We  have  seen  (page  u)  that  the  deviation  produced  by  a  prism  cor- 
responds nearly  to  half  its  angle.  If  we  can  overcome  a  prism  of  six 
degrees,  apex  outwards,  it  is  equivalent  to  saying  that  we  can  make  the 
visual  line  diverge  three  degrees.  This  manner  of  indicating  the  degree 
of  deviation  is  the  simplest,  and  that  which  is  most  frequently  used. 
It  has  been  attempted  to  introduce  another  notation  first  described  by 
Javal,  and  afterwards  adopted  by  Nagel.  This  author  names  meter  angle 
the  deviation  which  one  of  the  visual  lines  under- 
goes when,  after  having  fixed  a  point  at  infinity, 
we  look  at  a  point  situated  at  one  meter  distance 
on  the  visual  line  of  the  other  eye.  a>  (fig.  182)  isr 
therefore,  a  meter  angle,  if  A  is  situated  at  a  dis- 
tance of  one  meter;  two  meter  angles,  if  A  is  at 
50  centimeters,  and  so  forth.  The  system  was  in- 
vented to  measure  the  convergence  in  a  manner 
analogous  to  the  measurement  in  dioptrics  which 
we  use  for  refraction  (accommodation).  The  meter 
angle  corresponds  to  about  three  degrees  and  a 
half.  —  This  system  seems  to  offer  scarcely  any 
advantages,  and  it  has  this  quite  serious  disad- 
vantage, that  the  value  of  a  meter  angle  is  not  the 
same  for  different  persons.  It  varies  with  the 
base  line. 

We  call  by  this  name  the  distance  between  the  centers  of  rotation 
of  the  two  eyes ;  it  varies  between  66  mm.  and  58  mm.,  or  still  less.  We 
can  measure  it  by  sighting  a  distant  object,  a  lightning  rod  for  example, 
along  the  surface  of  a  planchette  held  horizontally.  We  close  one 
eye  and  fix  a  needle  in  the  planchette,  so  that  it  may  appear  to  coincide 
with  the  lightning  rod.  The  needle  must  not  be  placed  too  near  the  eye 


Fig.  182. 


THE  OCULAR  MOVEMENTS  303 

in  order  that  its  images  may  not  be  too  diffuse.  Then  we  repeat  the 
experiment  with  the  other  eye  without  displacing  the  head ;  opening  the 
two  eyes,  we  should  see  the  two  needles  blended  into  one,  which  coin- 
cides with  the  lightning  rod.  The  distance  between  the  needles  is  equal 
to  the  base  line.  —  We  find  also  very  great  variations,  especially  if  we 
examine  children,  whose  base  line  is  manifestly  very  short. 

Now  it  is  clear  that  the  deviation  which  the  eye  must  undergo,  in 
order  to  pass  from  infinity  to  one  meter  distance,  is  so  much  more  con- 
siderable in  proportion  as  the  base  line  is  greater.  —  A  meter  angle  cor- 
responds to  3°4o'  for  a  person  who  has  a  base  line  of  64  mm.,  to  3°2o'  if 
the  base  line  is  58  mm.  To  do  well,  therefore,  it  would  be  necessary 
each  time  we  measure  the  convergence  in  meter  angles,  to  tell  also  the 
length  of  the  base  line. 

Prentice  proposed  to  number  prisms  according  to  the  linear  deviation 
which  they  produce  at  a  given  distance,  observing  that  at  a  distance  of 
one  meter  the  deviation  produced  by  a  prism  of  one  degree  is  about 
one  centimeter. 

123.  Relations  between  Accommodation  and  Convergence.  —  In  the 

interest  of  single  and  distinct  vision,  it  is  necessary  that  there  be  formed 
on  each  favea  a  distinct  image  of  the  object  fixed.  In  order  that  the 
images  be  formed  on  the  two  foveas,  it  is  necessary  that  the  individual 
make  his  eyes  converge  towards  the  observed  object,  and  in  order  that 
the  images  be  distinct,  it  is  necessary  that  each  accommodate  exactly 
for  the  object.  There  is  thus  formed  a  relation  between  accommodation 
and  convergence,  so  that  we  cannot  easily  converge  towards  an  object 
without  also  accommodating  for  this  object.  The  rule,  however,  is  not 
absolute;  we  can,  if  it  is  necessary  for  distinctness  of  vision,  change 
within  certain  limits  the  degree  of  accommodation  without  changing 
the  degree  of  convergence.  This  play  of  the  accommodation,  which  is 
possible  while  the  convergence  remains  the  same,  has  the  name  relative 
amplitude  of  accommodation  (Bonders).  We  can  measure  this  amplitude 
by  placing  convex  and  concave  glasses  before  the  eyes  until  the  object 
appears  double  or  diffuse. 

Bibliography.  —  Javal  (E.).  In  de  Wecker.  Trait  $  des  maladies  des  yeux.  Paris,  1866. 
—  Donders.  Anomalies  of  tie  Refraction  of  the  Eye.  London,  1864.  —  Nagel  (A.).  Ueber  die 
Seziehungen  dioptriscker  Werthe  und  der  Betrage  symmetrischer  Convergenzbeu'egungen  nach  mc- 
trisc.hen  Einhciten.  Mittheilunr/en  aus  der  opktalmiatrischen  Klinik  in  Tubingen.  Tubingen,  1880. 
Lamare.  Les  mouvemenfs  des  yeux  dans  la  lecture.  Evil,  de  la  Soc.fr.  d'opht.  1882,  p.  354.  — 
Prentice  (Ch.  F.).  Ein  metrisches  System  zur  Bezeichnung  IL.  Bestimmwng  v.  Prismen.  Archir. 
/.  Augenheilk.  XXII,  p.  215. 


CHAPTER   XXI. 
THE  PROJECTION  OF  VISUAL  IMPRESSIONS. 

124.  Projection  Outwards  in  TJniocular  Vision.  —  In  order  to  be  able 
to  form  a  correct  idea  of  the  position  of  an  exterior  object,  it  is  neces- 
sary to  be  informed  as  to  the  direction  and  distance  of  this  object.  Judg- 
ment of  the  direction  is  formed  as  well,  or  better,  with  a  single  eye; 
the  superiority  of  binocular  vision  is  apparent  in  the  judgment  of  dis- 
tance, but  at  the  same  time,  in  the  matter  of  direction,  it  causes  certain 
illusions  from  which  persons  blind  of  one  eye  are  exempt.    We  shall  first 
discuss  the  vision  of  these  latter. 

GENERAL  LAW  OF  PROJECTION.  —  An  impression  of  any  point  of  the 
retina  is  projected  outwards  into  the  visual  field,  following  the  line  of 
direction;  that  is  to  say,  following  a  straight  line  passing  through  the 
retinal  point  and  the  nodal  point  of  the  eye.  We  have  seen  that  in- 
versely, an  exterior  point  for  which  the  eye  is  focused  forms  its  image 
at  the  point  of  intersection  of  the  line  of  direction  with  the  retina.  As 
long  as  there  is  question  only  of  objects  seen  distinctly,  the  law  of  pro- 
jection is  equivalent  to  saying  that  we  see  exterior  objects  in  the  direc- 
tion in  which  they  really  are.  The  law  of  projection  does  not  apply 
merely  to  the  ordinary  phenomena  of  vision :  all  the  retinal  impressions, 
the  phosphenes,  after  images,  entoptic  phenomena,  circles  of  diffusion, 
etc.,  are  projected  according  to  this  law,  which  is  entirely  general. 
As  exceptions  we  can  cite  only  the  deformities  of  objects  seen  indi- 
rectly, which  seem  to  show  that  the  law  is  not  followed  very  exactly 
for  very  peripheral  parts  of  the  retina,  and  perhaps  for  some  of  the  illu- 
sions which  I  shall  mention  later. 

125.  Projection  of  the  Visual  Field.  —  The  law  which  we  have  just 
announced  regulates  the  manner  in  which  we  localize  objects  in  the 

304 


THE  PROJECTION  OF   VISUAL  IMPRESSIONS  305 

visual  field,  but  it  does  not  regulate  the  projection  of  the  visual  field  in 
its  entirety.  The  latter  depends  on  the  manner  in  which  we  judge  the 
position  of  the  eye,  or  rather  the  direction  of  the  visual  line.  If  in 
uniocular  vision,  we  judge  correctly  the  direction  of  the  visual  line,  the 
entire  visual  field  is  projected  in  a  correct  manner.  We  shall,  therefore, 
proceed  to  discuss  the  means  by  which  we  form  this  judgment. 

Supposing  that  we  fix  a  point  A,  and  that  we  desire  to  fix  another 
point  B.  As  long  as  we  fix  A,  B  is  seen  in  indirect  vision,  and  the  dis- 
tance between  the  images  enables  us  to  judge  of  the  degree  of  innerva- 
tion  necessary  to  bring  the  look  towards  B ;  generally  this  judgment  is 
quite  exact  so  that  we  bring  the  look  towards  B  almost  without  hesita- 
tion. From  innervation  results  the  contraction  of  the  muscles,  the 
change  of  position  of  the  eye  and  the  change  of  the  retinal  image  until 
B  forms  its  image  on  the  fovea.  —  One  might  think  that  the  sensation 
of  the  moie  or  less  considerable  contraction  of  the  muscles,  the  gliding 
of  the  eye  between  the  lids,  etc.,  could  furnish  us  with  information  on 
the  direction  of  the  visual  line,  but  this  is  not  so;  we  judge  this  direc- 
tion solely  by  the  degree  of  innervation  which  we  have  used  to  bring  the 
look  into  this  direction.  This  fact  is  well  established  by  the  observation  of 
patients  affected  with  ocular  paralysis.  If,  for  example,  we  tell  a  patient 
affected  with  paralysis  of  the  right  external  rectus  to  close  his  left  eye 
and  look  to  the  right,  he  furnishes  the  innervation  necessary;  the  eye 
remains  motionless  on  account  of  the  paralysis,  but  the  patient  thinks  he 
has  moved  it  to  the  right,  so  that  there  results  a  false  projection;  if  we 
tell  the  patient  to  move  his  finger  rapidly  towards  an  object  situated 
to  the  right,  not  having  time  to  guide  himself  by  the  sight  of  the  finger, 
he  constantly  moves  it  too  far  to  the  right.  A  healthy  person  can  make 
the  experiment  by  looking  to  one  side,  while  he  exerts  a  traction  in 
the  opposite  direction  on  a  fold  of  the  skin,  near  the  external  canthus. 
The  traction  is  communicated  by  the  conjunctiva  to  the  globe,  and  on 
account  of  the  resistance  which  it  exerts,  one  is  obliged  to  use  a  stronger 
innervation  to  bring  the  look  to  the  opposite  side;  we  conclude  from 
this  that  the  look  is  carried  farther  in  this  direction  than  it  really  is, 
which  causes  projection  of  the  visual  field  in  a  false  manner. 

Judgment  of  the  degree  of  innervation  used  is  very  exact,  because  it 
is  always  corrected  by  the  result  obtained,  as  the  following  experiment 
shows.  One  looks  directly  in  front  after  having  put  a  prism  of  ten  de- 
grees, apex  to  the  left,  before  each  eye.  Seen  through  the  prisms,  an 
object  situated  at  ten  degrees  to  the  right,  appears  five  degrees  from  the 


3C6  PHYSIOLOGIC   OPTICS 

visual  line,  and  we  need  only  an  innervation  corresponding  to  five  de- 
grees to  fix  it ;  we  think,  therefore,  that  it  is  situated  at  five  degrees  to 
the  right,  and,  if  we  wish  to  grasp  it,  we  do  not  bring  the  hand  far 
enough  to  the  right.  But  it  suffices  to  repeat  the  experiment  only  a  few 
times  in  order  to  be  no  longer  deceived :  we  learn  very  quickly  to  reckon 
with  prisms.  If  then  we  repeat  the  experiment  after  having  removed 
them,  we  bring  the  hand  too  far  to  the  right. 

When  we  judge  correctly  the  direction  of  the  visual  line  there  is  in 
monocular  vision  no  possible  illusion  as  to  the  direction  in  which  objects 
are.  In  mathematics  we  often  determine  the  position  of  a  point  by 
means  of  what  are  called  polar  coordinates.  Being  given  a  fixed  point, 
named  center  of  coordinates,  the  position  of  any  other  point  is  determined 
by  the  direction  and  length  of  the  radius  vector,  that  is  to  say,  of  the  line 
which  joins  the  two  points.  In  uniocular  vision,  the  center  of  coordi- 
nates is  represented  by  the  eye,  or,  more  exactly,  by  its  nodal  point ;  the 
law  of  projection  gives  the  direction  of  the  radius  vector.  To  know  the 
exact  position  of  the  exterior  point,  there  is  wanting,  therefore,  only 
the  length  of  the  radius  vector,  but  this  the  eye  does  not  give,  at  least 
not  in  a  direct  manner. 

It  is  easy,  indeed,  to  convince  oneself  that  while  the  eye  informs  us 
very  exactly  on  the  direction  in  which  the  light  comes,  it  gives  us  no 
information  as  to  the  distance  whence  it  comes.  The  information  which 
the  greater  or  less  degree  of  accommodation  used  could  furnish  is  too  in- 
definite. —  In  the  tenth  chapter  I  laid  stress  on  the  importance  which  the 
study  of  the  form  under  which  a  distant  luminous  point  is  seen  may  have 
in  the  matter  of  exact  knowledge  on  the  optics  of  the  eye.  One  might 
think  that  one  can  replace  the  distant  luminous  point  by  a  near  luminous 
point  placed  at  the  focus  of  a  strong  lens.  If  the  eye  would  inform  us 
on  the  distance  whence  the  light  comes  to  it,  the  result  of  the  two  ex- 
periments ought  to  be  the  same,  since  the  rays  reaching  the  eye  are 
parallel  in  both  cases.  But  this  is  not  so.  Other  information  tells  us,  in 
fact,  that,  in  the  latter  case,  the  luminous  point  is  very  near,  which  makes 
us  see  the  figure  of  diffusion  extremely  small,  and  makes  this  form  of 
experiment  not  to  be  recommended.  —  We  know  also  that  the  after 
images  appear  to  us  large  or  small,  according  as  we  project  them  on 
a  distant  or  near  surface,  which  shows  clearly  that  the  eye  does  not 
accord  to  them  a  real  distance.  If  we  do  not  present  to  them  a  surface 
on  which  they  can  be  projected,  for  example  by  closing  the  eyes,  they 
generally  seem  to  have  the  same  apparent  size  as  the  object  of  which 
they  are  the  image;  we  accord  to  them  the  distance  of  this  object,  a 


THE  PROJECTION  OF  VISUAL  IMPRESSIONS  307 

distance  which  is  not  told  by  a  direct  sensation,  but  which  we  judge  by 
an  unconscious  reasoning,  as  we  shall  see  in  the  following  chapter. 


126.  Projection  in  Binocular  Vision.  —  The  impressions  of  the  two 
macula  arc  projected  towards  the  same  place.  When  the  eyes  perform  their 
functions  correctly,  both  of  them  always  fix  the  same  object,  so  that 
under  these  circumstances  the  fact  stated  is  not  surprising.  But  it  is 
the  same  when  they  do  not  fix  the  same  object,  as  is  evident  among 
others  from  stereoscopic  experiments.  The  following  experiment  seems 
to  me  to  demonstrate  this  fact  in  a  very  striking  manner,  but  it  is  neces- 
sary to  be  able  to  squint  in  order  to  repeat  it.  It  is  quite  easy  to  learn 
to  squint  inwards;  in  order  to  squint  outwards  we  take  hold  of  a  fold 
of  the  skin  near  the  outer  canthus  of  one  eye,  while  we  look  towards 
the  opposite  side.  —  To  perform  the  experiment,  we  close  one  eye  and 
look  at  the  flame  with  the  other,  so  as  to  produce  an  after  image.  We 
then  open  the  closed  eye  and  select  a  point  which  we  fix  with  this  eye 
while  we  are  endeavoring  to  squint.  We  then  see  the  after  image  place 
itself  on  the  point  of  fixation,  although  the  visual  line  of  the  eye  to  which 
it  belongs  is  not  at  all  directed  towards  this  point.  We  can  squint  more 
or  less  considerably,  placing  the  visual  line  in  divergence  or  in  con- 
vergence :  as  long  as  the  other  eye  fixes  the  point  of  fixation,  the  after 
image  is  located  there  also. 

PHYSIOLOGIC  BINOCULAR  DIPLOPIA.  —  Let  A,  figure  183,  be  an  ob- 
ject which  both  eyes  fix,  B  another  nearer  object.  If  we  close  the  right 
eye,  the  point  B  is  seen  five  degrees  to  the  right  of  A ;  if  we  close  the 
left  eye,  it  is  seen  five  degrees  to  the  left  of  A.  Opening  both  eyes,  A 
is  seen  single  at  the  place  where  it  really  is;  we  see  two  images  of  B, 
one  five  degrees  to  the  left,  the  other  five  degrees  to  the  right  of  A.  — 
We  therefore  see  B  in  double  crossed  images;  if  we  fix  B,  A  is  pre- 
sented in  double  homonymous  images.  —  We  can  perform  the  experi- 
ment with  two  candles,  and,  if  necessary,  we  can  make  the  diplopia  more 
striking  by  placing  a  red  glass  in  front  of  one  eye. 

This  singular  phenomenon,  which  had  already  been  described  by 
Alhasen,  is  known  as  physiologic  binocular  diplopia. 

CENTER  OF  PROJECTIONS.  —  We  observe  that  the  correct  information 
which  the  eyes  furnish  to  us  gives  rise  to  a  false  interpretation,  for  it  is 
evident  that,  when  an  object  is  seen  double,  there  is  at  least  one  of  the 
images  which  does  not  coincide  with  the  object.  When  we  close  one  eye, 


308 


PHYSIOLOGIC  OPTICS 


the  corresponding  image  disappears, 
"*"'?  while  the  other  image  does  not  change 
position.  The  false  judgment  must, 
therefore,  persist  also  in  this  case,  at 
least  for  one  of  the  eyes.  The  sight 
of  normal  persons  does  not,  therefore, 
necessarily  become  similar  to  that  of 
a  one-eyed  person. 

The  physiologic  diplopia  is  due  to 
the  fact  that  we  do  not  take  into  con- 
sideration the  different  position  of  the 
two  eyes;  without  a  special  examina- 
tion we  cannot  tell  whether  an  image 
belongs  to  one  eye  or  the  other. 
We  refer  every  visual  impression, 
from  whatever  eye  it  may  come, 
to  a  common  and  single  center, 
which,  in  my  case,  coincides  pretty 
exactly  with  the  right  eye.  Recall- 
ing the  mathematical  terms  which  we 
have  used  in  the  preceding  chapter,  we  may  say  that  it  is  the  center 
of  the  coordinates  the  position  of  which  we  judge  imperfectly.  If  we 
took  into  account  the  different  position  of  the  two  eyes,  we  would  have 
two  centers  of  coordinates,  and  the  idea  of  the  direction  of  the  object 
would  suffice  to  fully  determine  its  position.  In  the  experiment  (fig. 
183)  we  would  thus  reason  as  follows:  Since  we  see  with  the  right  eye 
an  object  five  degrees  to  the  left  of  A,  with  the  left  eye  the  same  object 
five  degrees  to  the  right  of  A,  the  object  must  be  in  the  midjile  plane 
and  nearer  than  A;  we  would  therefore  see  B  single  and  in  its  right 
place.  Instead  of  this  we  refer  the  impressions,  as  in  uniocular  vision, 
to  a  single  center,  and  we  inform  ourselves  that  the  object  must  be 
double,  since  it  is  seen  at  once  to  the  right  and  the  left. 

DIRECTING  EYE.  (i)  —  In  my  case  this  center  of  coordinates  coincides 
almost  exactly  with  the  right  eye,  probably  because,  having  used  it  so 
much  separately,  I  have  acquired  the  faculty  of  judging  exactly  with 
this  eye  the  position  of  exterior  objects,  or,  in  other  words,  because 
there  is  developed  a  kind  of  uniocular  vision  in  addition  to  binocular 


Fig.  183. 


(1)  According  to  a  communication  from  Javal,  the  binocular  vision  of  Vallee  was  like  mine.  He  de- 
scribed this  condition  as  general  (in  a  communication  to  the  Academy  of  Sciences,  about  1830),  and  gave 
the  name  directing  eye  to  the  eye  which  controls  projection  outwards.  H.  Kaiser  has  also  described  the 
same  condition  for  his  eyes. 


TEE  PROJECTION  OF  VISUAL  IMPRESSIONS  309 

vision.  I  must  add,  however,  that  this  condition  was  not  developed  as 
a  result  of  my  labors  on  physiologic  optics,  because  the  phenomena 
were  the  same  when,  twelve  years  ago,  I  began  to  devote  my  attention 
to  this  subject.  According  to  Hering  the  center  is  often  at  an  equal  dis- 
tance between  the  two  eyes,  and  this  would,  in  fact,  be  the  true  type  of 
binocular  vision,  in  which  neither  of  the  eyes  plays  a  dominant  part.  — 
The  reasons  why  I  say  that  in  my  case  the  center  of  projections  coin- 
cides with  the  right  eye,  are  as  follows : 

i°  When  on  looking  at  a  distant  object  I  see  a  near  object  in  double 
crossed  images,  and  when  I  try  to  touch  this  object  by  a  quick  motion, 
I  grasp  it  correctly  if  I  sight  the  image  with  the  right  eye,  while  I  bring 
the  hand  far  from  the  object  if  I  sight  the  image  with  the  left  eye.  It 
is  the  same  if  I  close  one  eye.  With  the  right  eye  I  judge  accurately  the 
position  of  objects  seen  indirectly,  as  a  one-eyed  person  would  do;  with 
the  left  eye  I  judge  falsely.  Thus,  in  the  experiment  figure  183,  closing 
the  right  eye,  I  see  B  five  degrees  to  the  right  of  A,  as  I  ought  to,  but 
I  refer  the  impression  to  my  right  eye,  and,  thinking  that  the  object  B 
is  five  degrees  to  the  right  of  the  visual  line  of  my  right  eye,  in  order  to 
reach  it  I  bring  my  hand  towards  Bx.  —  I  have  also  noticed,  especially 
when  I  observe  the  double  images  of  near  objects,  accidentally  and  with- 
out trying  to,  that  one  of  them,  that  of  the  right  eye,  presents  a  more 
material  appearance,  while  the  other  rather  resembles  a  kind  of  shadow ; 
Dr.  Knapp,  Jr.,  made  the  same  remark  to  me.  It  must  be  noted  that 
my  eyes  are  practically  equal,  as  to  acuity  and  refraction. 

2°  I  fix  a  mark  P  (fig.  184),  not  too  bright,  placed  on  a  dark  and  uni- 
form background.  Interposing  a  stick  between  my  eyes  and  the  back- 
ground, on  the  visual  line  of  the  right  eye,  I  see  it  in  double  images; 
the  image  of  the  right  eye  (d)  coincides  with  the  mark  of  fixation,  while 
the  image  of  the  left  eye  is  seen  more  to  the  right  (g)  (fig.  184  A).  If 
now  I  fix  the  stick,  it  is  the  image  g  of  the  left  eye  which  is  brought 
towards  that  of  the  right  eye  d,  in  order  to  coincide  with  it,  while  the 
latter  remains  motionless.  One  might  think  that  this  is  due  to  the  fact 
that  I  placed  the  stick  on  the  visual  line  of  the  right  eye,  but  this  is  not 
so;  if  I  place  the  stick  on  the  visual  line  of  the  left  eye  (fig.  184,  B)  so 
that  the  image  of  the  right  eye  d  is  seen  to  the  left,  it  is  still  the  latter 
which  remains  motionless,  while  that  of  the  left  eye  makes  a  great  move- 
ment to  join  itself  to  it  when  I  fix  the  stick.  —  This  apparent  movement 
exists  also  when  I  close  the  right  eye,  although,  under  these  circum- 
stances, the  left  eye  does  not  make  any  movement.  Under  this  latter 
form  the  experiment  was  described  by  Hering. 


310 


PHYSIOLOGIC   OPTICS 


3°  This  author  furthermore  described  the  following  experiment:  we 
fix  binocularly  an  object  placed  at  some  distance  in  the  median  plane, 
and  we  try,  by  a  quick  movement,  to  place  a  stick  quite  near  the  face  in 
the  direction  in  which  we  see  the  object;  it  is  better  to  conceal  the 
movement  of  the  hand  with  a  screen.  Making  this  experiment,  I  bring 
the  stick  pretty  exactly  on  the  visual  line  of  the  right  eye.  The  experi- 
ment is  easy  to  repeat  even  with  persons  who  are  not  accustomed  to 
study  such  questions,  and  we  can  control  by  placing  ourselves  in  front 
of  the  observed  person  and  sighting  with  one  eye  along  the  mark  of 
fixation  and  the  space  between  the  eye-brows  (glabella)  of  the  observed 


Fi?.  184. 

person.  I  have  observed  several  persons  in  this  way.  Most  of  them 
show  a  marked  tendency  to  prefer  one  or  other  eye,  which  seems  to 
indicate  a  tendency  to  a  development  of  a  uniocular  vision  in  addition  to 
the  binocular  vision  like  that  which  I  have  described  for  my  eyes.  Per- 
sons enjoying  pure  binocular  vision  must  place  the  stick  in  the  median 
plane;  as  the  center  of  projection  does  not  coincide  with  either  of  the 
eyes,  these  people  cannot  project  correctly  objects  seen  indirectly.  This 
type  of  vision,  therefore,  seems  inferior  to  the  other,  as  far  as  orienta- 
tion is  concerned. 

HOROPTER.  —  All  the  points  outside  the  point  fixed  are  not  seen 
double;  the  point  C  (fig.  183),  for  example,  is  seen  ten  degrees  to  the 
right  of  A,  as  well  with  the  right  eye  as  with  the  left  eye ;  it  is  therefore 
seen  single.  —  The  entirety  of  the  points  seen  single  while  we  fix  a  given 


THE  PROJECTION  OF  VISUAL  IMPRESSIONS 


311 


point,  is  called  horopter.  —  The  study  of  the  horopter  is  quite  a  compli- 
cated mathematical  problem,  and  without  much  interest,  since  the  di- 
plopia  is  only  very  slightly  indicated  when  the  object  is  a  little  distant 
from  the  point  of  fixation.  It  may  be  solved  when  we  know  the  posi- 
tion of  the  corresponding  points  (see  the  following  chapter)  and  the  law 
which  regulates  the  position  of  the  eyes  (law  of  Listing).  When  the  point 
of  fixation  is  in  the  plane  which  contains  the  primary  position  of  the 
visual  lines,  we  see  single  all  the  points  which  are  on  a  circle  passing 
through  the  point  of  fixation  and  the  nodal  points  (horopter  of  Johannes 


Fig.  185. — Horopter  of  Johannes  Miiller. 

Mutter,  fig.  185).  It  is  easy  to  see  that  on  fixing  A,  B  is  seen  single, 
because  the  two  angles  designated  by  a  are  equal,  since  both  correspond 
to  the  arc  AB.  —  If  we  fix  a  point  on  the  floor,  situated  in  the  median 
plane,  the  horopter  corresponds  almost  to  the  plane  of  the  floor. 

SUPPRESSION  OF  DOUBLE  IMAGES.  —  As  one  sees  some  exterior 
objects  double,  and  some  single,  one  might  think  that  it  would  re- 
sult in  great  confusion.  It  does  not :  most  people  have  never  observed 
double  physiologic  images  before  making  the  experiment  described 
above.  Under  ordinary  circumstances  the  attention  is  always  brought 
to  bear  on  the  object  fixed,  and  the  look  never  remains  for  any  length 
of  time  on  the  same  object,  so  that  we  have  not  much  time  to  perceive 


312  PHYSIOLOGIC  OPTICS 

double  images.  It  must  also  be  observed  that  the  objects,  not  fixed, 
form  their  images  on  the  peripheral  parts  of  the  retina,  where  the  per- 
ception is  less  distinct  than  at  the  macula.  It  is  scarcely  possible  to  sup- 
pose a  serviceable  binocular  vision  if  the  entire  retina  had  an  acuity  like 
that  of  the  fovea.  But  we  also  make  important  use  of  the  phenomenon 
known  under  the  name  of  neutralization  of  images,  and  which  has  been 
given  special  prominence  by  the  works  of  Javal  on  the  vision  of  persons 
affected  with  strabismus  (see  chapter  XXIII). 

In  addition  to  the  fact  that  most  of  the  time  an  object  seems  to  be 
at  two  different  places,  binocular  vision  gives  rise  to  yet  another  con- 
tradiction. Making  the  experiment  with  the  two  candles  before  the 
screen  DE  (fig.  183),  we  have  seen  that  the  right  eye  sees  the  candle  B 
at  five  degrees  to  the  left  of  A ;  in  this  direction  the  left  eye  sees  a  part 
of  the  screen;  and  as  we  do  not  take  into  consideration  the  different 
position  of  the  two  eyes,  but  refer  our  impressions  to  a  common  center, 
the  result  is  that  we  seem  to  see  two  objects  in  the  same  direction. 
Interposing  a  stick  between  the  eyes  and  a  book  (controlled  reading  of 
Javal)  we  can  read  without  interruption  only  when  both  eyes  are  open ; 
if  we  close  one  eye,  the  stick  covers  some  of  the  characters.  We  here 
meet  the  same  contradiction;  we  see  the  stick  in  the  same  direction  as 
the  characters  which  it  conceals,  and  as,  on  the  other  hand,  we  know  that 
it  is  nearer  than  the  book  it  appears  transparent.  But,  in  cases  in  which 
such  an  interpretation  is  not  possible,  for  example  when  we  present  to 
both  eyes  wholly  different  images,  in  a  stereoscope,  we  observe  what  is 
called  antagonism  of  the  visual  fields.  It  is  sometimes  the  images  of  one 
eye  that  predominate,  sometimes  those  of  the  other,  and  as  long  as  we 
see  in  a  part  of  the  visual  field  images  of  one  eye,  those  of  the  other  are 
completely  suppressed. 

It  seems  that  this  suppression  of  the  images  of  one  eye  plays  a  great 
part  in  binocular  vision,  and  that  it  is  this  which  generally  causes  us 
not  to  observe  double  physiologic  images.  —  It  is  not  easy  to  know 
which  of  the  two  images  is  suppressed,  for  as  soon  as  we  pay  attention 
to  this  question  both  appear.  Generally  it  is  the  more  eccentric  image, 
or,  in  other  cases,  the  image  which,  on  account  of  the  perspective,  occu- 
pies the  smallest  retinal  surface  (Javal)  which  disappears.  But,  in  most 
persons,  there  seems,  as  I  have  already  stated,  to  be  developed  a  certain 
superiority  of  the  eye  which  is  most  frequently  used  separately,  and 
then  it  is  always  the  image  of  the  other  eye  which  is  suppressed. 

Bibliography.  —  M  uller  (Johannes).  Beitrage  zur  vergleicJienden  Physiologic  des  Gesichis- 
sinnes.  Leipzig,  1826.  —  Hering  (E.).  Beitrage  zur  Physiologic.  Leipzig,  1861.  — Kaiser 
(H.).  Compendium  der  physiologischen  Optik.  Wiesbaden,  1872,  p.  298. 


CHAPTER   XXII. 

MONOCULAR  PERCEPTION  OF  DEPTH 

127.  Influence  of  Accommodation.  —  I  have  already  said  that  the  eye 
gives  us  no  direct  information  as  to  the  distance  from  which  light  comes 
to  it.    We  might  think  that  the  degree  of  accommodation  used  in  order 
to  see  the  object  distinctly  would  inform  us  as  to  its  distance.  When  the 
eye  is  accommodated  for  distant  objects,  near  objects  do  not  appear  dis- 
tinct, and  an  experienced  observer  might  use  this  circumstance  to  judge 
of  the  distance  of  an  object.     Young  said  that  painters  must  take  care 
to  show  near  objects  vaguely  under  penalty  of  obtaining  a  hard  and  dis- 
agreeable effect.    But  the  importance  of  accommodation  for  the  judg- 
ment of  distance  is  but  small,  because,  generally,  we  are  dealing  with 
such  long  distances  that  the  difference  of  accommodation  is  insignificant. 
For  all  distances  exceeding  one  meter,  the  variation  of  accommodation 
does  not  reach  one  dioptry. 

128.  Indirect  Judgment  of  Distance.  —  In  the  absence  of  direct  in- 
formation, a  whole  series  of  circumstances  enable  us  to  judge  of  the 
distance  of  an  object,  generally  by  an  unconscious  judgment. 

a.  The  knowledge  of  the  nature  of  objects  often  furnishes  us  with  a 
means  of  knowing  their  distances.  Thus,  if  we  know  the  size  of  an  ob- 
ject, we  can  judge  its  distance  from  its  angular  size.  It  is  the  size  of 
man  especially  which  enables  us  to  make  this  judgment.  Generally  we 
judge  directly  of  distance.  When  we  see  a  man  very  far  off,  he  does  not 
appear  to  us  small,  because  we  know  what  size  he  ought  to  be,  but  we 
conclude  that  he  must  be  very  far  away,  since  the  angular  size  is  small, 
and  this,  without  this  latter  fact  directly  striking  our  consciousness. 
This  observation  is  quite  characteristic  of  the  manner  in  which  un- 
conscious judgments  are  formed,  and  it  must  be  noted  that  this  way  of 
judging  is  something  to  be  learned.  I  recall  very  well  that  the  first  time 
I  saw  a  man  climb  the  mast  of  a  ship,  he  appeared  to  me  like  a  doll, 

313 


314  PHYSIOLOGIC   OPTICS 

and  Helmholtz  reports  a  similar  observation.  —  If  we  look  at  distant 
objects  through  a  telescope  they  are  enlarged;  but  as  long  as  we  have 
to  do  only  with  objects  of  known  size,  such  as  men,  houses,  etc.,  they 
seem  to  preserve  their  natural  size,  but  appear  near.  We  must  open  the 
other  eye  to  convince  ourselves  that  they  are  really  enlarged. 

b.  A  means  which  is  often   used  to  judge  whether  one   object   is 
nearer  than  another,  is  to  observe  whether  it  conceals  a  part  of  the 
other.     If  one  hill  conceals  the  lower  part  of  another  hill  it  must  be 
nearer. 

c.  If  we  are  acquainted  with  the  object  at  which  we  are  looking,  or  if 
there  is  a  certain  regularity,  we  easily  come  to  know  what  part  is  nearest. 
On  the  photograph  of  a  house,  we  easily  judge  the  distance  at  which 
the  different  parts  ought  to  be,  while  photographs  of  rocks,  landscapes, 
etc.,  are  frequently  more  difficult  to  interpret. 

d.  The  shadows  thrown  are  often  important  for  the  judgment  of  dis- 
tance.   If  a  surface  is  illuminated,  the  luminous  source  must  be  in  front 
of  it,  and  if  an  object  casts  a  shadow  on  this  surface,  it  must  be  nearer 
the  observer  than  the  surface.     It  is  for  this  reason  that  we  obtain  a 
much  better  idea  of  the  reality  by  adding  shading  to  a  drawing. 

e.  Finally,  aerial  perspective  sometimes  influences  the  idea  which  we 
form  of  distance.     We  comprise  under  this  term  the  darkening  and 
change  of  color  which  distant  objects  undergo  on  account  of  the  in- 
complete transparency  of  the  layers  of  air  which  separate  them  from  the 
observer.    The  vapors  of  water  which  are  in  the  atmosphere  reflect  the 
blue  rays,  and  allow  the  red  rays  to  pass.    Comparing  the  spectra  of  a 
blue  sky  and  a  cloudy  sky,  Lord  Rayleigh  thus  found  that  the  brightness 
of  the  latter  diminishes  greatly  towards  the  blue  extremity.   When  the 
spectra  had  the  same  brightness  in  the  red,  the  green  of  the  cloudy  sky 
was  already  less  strong  than  that  of  the  blue  sky.    It  is  for  this  reason 
that  the  setting  sun  appears  red,  and  distant  mountains  blue.  When  there 
is  much  water  vapor  in  the  atmosphere,  we  see  distant  objects,  such  as 
forests  and  hills,  more  distant  and  consequently  larger  than  they  really 
are.    In  the  mountains  the  air  is,  as  a  rule,  very  pure,  which  causes  us 
to  often  judge  the  distance  and  height  of  the  summits  much  smaller 
than  they  really  are. 

We  know  that  the  sun  and  moon  appear  larger  when  they  are  near 
the  horizon,  which  is  merely  an  illusion.  If  we  measure  their  angular 
size,  we  find  it  exactly  the  same  in  both  cases.  Likewise,  if  we  try  to 
divide  the  distance  between  the  zenith  and  the  horizon  into  two  equal 
parts,  we  are  greatly  deceived ;  the  lower  part  is  always  too  small.  Since 


MONOCULAR  PERCEPTION  OF  DEPTH  315 

the  moon,  near  the  horizon,  appears  larger  than  near  the  zenith,  although 
it  has  the  same  angular  size,  it  is  equivalent  to  saying  that  we  judge  it 
to  be  farther  away.  The  illusion  is  due  to  the  aerial  perspective.  The 
moon  is  seen  through  a  much  thicker  layer  of  the  terrestrial  atmosphere 
when  it  is  near  the  horizon  than  when  it  is  at  the  zenith.  It  seems,  how- 
ever, that  the  comparison  with  terrestrial  objects  also  plays  a  part  in 
this  judgment  (fig.  186). 

These  different  means  enable  us  to  judge  more  or  less  exactly  of  the 
distance  of  an  object.    They  are  especially  useful  to  us  when  we  have 


Fig.   186.  After  Young.  —  The  curve  indicates  the  apparent  form  of  the  sky.    The  sun, 
although  teen  under  the  same  angle,  seems  of  variable  size. 


to  do  with  long  distances,  on  which  the  parallax,  of  which  I  am  about  to 
speak,  cannot  give  any  information. 

129.  Influence  of  the  Parallax.  —  The  idea  which  we  obtain  of  the 
relief,  by  displacements  of  the  head,  is  well  known  to  all  who  use  the 
ophthalmoscope.  We  thus  obtain  a  very  distinct  idea  of  the  depth  of 
an  excavation,  etc.  —  We  often  use  this  means,  without  knowing  it,  to 
study  an  object  difficult  to  interpret,  and  it  is  the  principal  means  by 
which  one-eyed  people  account  for  the  relief.  The  observer  often  sees 
thus,  without  his  perceiving  that  he  does  so,  the  relative  movements  of 
exterior  objects,  and  he  uses  them  to  account  for  their  position.  If,  for 
example,  while  the  eye  is  displaced  from  a  to  b  (fig.  187)  the  observer 
sees  the  object  A  displaced  to  the  right  relatively  to  the  object  B,  A 
must  be  nearer  than  B ;  to  draw  this  conclusion,  we  need  not  look  dur- 
ing the  displacement.  If,  after  having  observed  the  objects  in  the  posi- 
tion a,  we  close  the  eye  to  open  it  again  only  in  the  position  b,  we  ob- 
serve, nevertheless,  that  A  has  changed  place  relatively  to  B,  which  suf- 
fices to  judge  of  its  distance. 

The  judgment  is  here  based  on  the  comparison  of  the  successive 
retinal  images ;  images  change  for  each  new  position  of  the  eye.  But, 


316  PHYSIOLOGIC  OPTICS 

xB  as  all  comparison  by  memory  is  defective,  we 
obtain  a  much  more  distinct  idea  of  the  differ- 
ence between  the  images,  and  consequently  of 
the  relief,  by  comparing  the  images  simultane- 
ously with  the  two  eyes,  and  it  is  for  this  rea- 
AX — >•  son  that  we  always  judge  distances  better  with 

two  eyes  than  with  one.  It  is  easy  to  convince 
ourselves  that  this  is  so  by  trying  to  reach  a 
stick  placed  at  some  distance  with  the  finger 
coming  from  the  side.  Looking  with  one  eye 
only  we  are  deceived  much  more  frequently  than 
when  we  open  both  eyes. 
^^  ^ —  When  we  look  with  the  two  eyes,  each  eye 

(       j  + (       j          receives  a  perspective  image  of  the  objects  situ- 

ji  ^7  ated  in  front  of  us;  as  the  two  eyes  are  not  at 

tig.  187.  the  same  place,  there  result  between  the  images 

differences  which  are  the  more  pronounced  the  smaller  the  distance  of 
the  object.  If,  on  the  contrary,  we  look  at  a  plane  image  with  both  eyes, 
the  retinal  images  are  identical.  This,  therefore,  is  a  sign  by  which  the 
appearance  of  an  object  of  three  dimensions  is  distinguished  from  a 
plane  image.  It  is  only  for  near  objects  that  this  difference  exists:  if  the 
objects  are  at  a  great  distance,  the  retinal  images  are  alike;  thus  a  land- 
scape presents  almost  the  same  appearance  whether  we  close  one  eye 
or  whether  we  open  both. 

Bibliography.  —  (Euvres  de  Young,  edited  by  Tsclierning,  p.  244. 


CHAPTER   XXIII. 
BINOCULAR  PERCEPTION  OF  DEPTH. 

130.  Influence  of  Convergence.  --  The  most  important  information  on 
the  distance  of  an  object  is  furnished  us  by  the  degree  of  convergence 
which  it  is  necessary  to  use  to  fix  it  binocularly.    Just  as  for  the  judg- 
ment of  the  direction  of  the  visual  line  in  uniocular  vision  (see  ch.  XXI), 
it  is  the  degree  of  innervation  used  which  guides  us,  and  not  at  all  the 
sensation  of  the  position  of  the  eyes,  which  is  always  very  vague.     It 
is  solely  for  differences  of  convergence  that  we  have  a  very  exact  sensa- 
tion; we  can  judge  with  very  great  exactness  whether  one  object  is 
nearer  or  farther  away  than  another;  the  judgment  of  absolute  distance 
is  very  uncertain.  —  When  we  fix  a  distant  object,  a  near  object  appears 
in  double  crossed  images.    Although  we  may  not  often  perceive  these 
images,  they  give  us,  nevertheless,  a  vague  idea  of  the  distance  of  the 
object,  for  they  suffice  to  give  a  pretty  accurate  impulse  to  convergence, 
since,  guided  by  them,  we  converge  for  the  object  without  much  effort. 
But  it  is  only  after  having  accomplished  convergence  and  having  seen 
that  the  innervation  given  has  attained  its  object,  that  we  have  an  accu- 
rate idea  of  the  distance.    The  difference  between  the  two  judgments 
is  almost  analogous  to  that  which  we  find  when  we  wish  to  measure 
the  distance  between  two  points.    Suppose  that  we  wish  to  measure  this 
distance  with  a  compass,  provided  with  a  scale  graduated  in  millimeters, 
telling  the  distance  between  the  two  points.     We  can  readily,  at  first 
sight,  give  to  the  compass  approximately  the  aperture  which  is  neces- 
sary, but  we  obtain  a  more  exact  and  distinct  idea  of  the  distance  when 
we  make  the  measurement  and  see  how  much  must  be  added  to  or  taken 
away  from  the  estimated  distance. 

131.  The  Stereoscope.  --  The  advantage  of  binocular  vision  was  made 
clear  only  by  the  invention  of  the  stereoscope  by  Wheatstme  (1833). 
With  this  instrument  we  obtain  an  impression  of  depth  much  superior 
to  that  which  any  other  representation  can  give  of  it. 

317 


318 


PHYSIOLOGIC   OPTICS 


Each  of  the  images  of  the  stereoscopic  representation  is  drawn  in  such 
a  way  as  to  form  in  the  eye  a  retinal  image  like  that  which  the  object 
would  form  there.  Distant  objects  are,  therefore,  represented  by  images 
which  are  identical,  while  the  images  of  near  objects  are  different. 

STEREOSCOPIC  PARALLAX.  —  In  order  to  account  for  the  manner  in 
which  objects  are  represented  on  stereoscopic  images,  we  may  suppose 
two  transparent  plates  (MM,  fig.  188),  placed  in  front  of  the  eyes  at  the 


Fig.  188. 

place  which  the  stereoscopic  image  will  occupy  later.  From  all  the  ex- 
terior points  we  suppose  straight  lines  directed  towards  the  eyes.  There 
start  thus  from  each  exterior  point  two  of  these  lines,  and  the  point 
at  which  each  of  these  straight  lines  cuts  the  corresponding  plate  is  the 
reproduction  of  the  exterior  point.  If  the  latter  is  at  infinity  the  two 
straight  lines  are  parallel,  and  the  distance  BB^  between  the  two  points, 
is  equal  to  the  base  line.  If  we  place  the  two  transparent  stereoscopic 
figures  one  over  the  other,  so  that  the  two  reproductions  of  the  same 
point  situated  at  infinity  overlap,  we  can  make  the  reproductions  of  all 
the  points  situated  at  infinity  coincide  two  by  two.  —  If,  on  the  con- 
trary, the  exterior  point  (C,  fig.  188)  is  not  at  infinity,  the  distance 
between  the  two  reproductions  is  less  than  that  of  the  eyes.  We  des- 
ignate the  difference  by  the  name  stereoscopic  parallax.  The  parallax 
of  the  point  C  is  BD  +  EID1  —  E.  Designating  the  distance  between 
the  two  eyes  by  b,  that  of  the  object  from  the  eyes  by  AO  =  d,  and  the 
distance  of  the  plate  from  the  eyes  by  g,  we  have 


BINOCULAR  PERCEPTION  OF  DEPTH  319 

b  —  E          b  E  bg 

-  =  -  r  =  -          or       E  =  -f- . 
d  —  g  d  y  d 

The  parallax  increases,  therefore,  with  the  distance  between  the  two 
eyes,  and  it  is  the  greater  as  the  object  is  nearer  the  observer. 

METHODS  OF  OBSERVING  THE  STEREOSCOPIC  IMAGES.  —  a.  Making 
the  visual  lines  parallel,  we  can  without  further  trouble  blend  the  two 
images  into  one,  which  appears  in  relief.  We  then  see  three  images, 
the  middle  one  of  which  gives  the  relief;  for  each  eye  sees  not  only  the 
image  which  is  intended  for  it,  and  which  is  blended  with  that  of  the 
other  eye,  but  also  the  image  which  is  intended  for  the  other  eye ;  we 
can  eliminate  the  two  useless  images  by  placing  the  hand  as  a  partition 
between  the  eyes.  It  may  be  difficult  to  make  the  visual  lines  parallel 
while  accommodating  for  a  quite  short  distance,  but  if  we  succeed  in 
doing  so,  the  illusion  is  as  perfect  as  with  the  stereoscope.  Frequently 
we  do  not  succeed  with  the  ordinary  stereoscopic  images  because,  be- 
ing intended  for  the  stereoscope  of  Brewster,  they  are  calculated  for 
too  long  a  base  line,  which  obliges  us  to  make  the  visual  lines  diverge 
in  order  to  fuse  them. 

We  can  also  look  at  the  images  by  directing  the  right  eye  towards  the 
image  of  the  left,  and  vice  versa,  so  that  the  visual  lines  intersect  at  a 
point  situated  in  front  of  the  image.  It  is  then  necessary  to  place  on  the 
left  the  image  intended  for  the  right  eye,  under  penalty  of  seeing  the 
relief  reversed,  if  the  supposed  object  lends  itself  to  such  an  interpreta- 
tion. —  The  fused  image  appears  diminished  and  situated  in  front  of 
the  plane  of  the  drawing,  at  the  point  of  intersection  of  the  visual  lines. 

b.  The  stereoscope  of  Wheat  stone,  the  first  which  was  constructed,  is 
composed  of  two  plane  mirrors  (bd  and  bdj,  forming  a  right  angle  (fig. 
189);  the  eye  OL  looks  into  the  mirror  on  the  right  at  the  image  of  the 
drawing  Bj  D1}  which  it  sees  at  ff^ ;  the  eye  O  sees  the  image  of  BD  at 
the  same  place ;  the  two  images  are  fused  into  a  single  one  presenting 
relief.     In  order  not  to  have  the  relief  reversed  or  pseudoscopic,  it  is 
necessary  to  present  to  the  left  eye  the  image  intended  for  the  right 
eye,  since  the  mirrors  reverse  the  images. 

c.  The  stereoscope  most  used  is  that  of  Brcwster:  each  eye  looks 
through  a  prism  with  convex  surfaces,  the  apex  of  which  is  turned 
towards  the  nose.     The  glasses  produce  a  certain  magnification,  and 
their  prismatic  effect  renders  it  unnecessary  to  make  the  visual  lines 
parallel. 

We  can  replace  the  glasses  of  the  stereoscope  of  Brewster  by  ordinary 
convex  lenses,  by  decentering  them ;  that  is  to  say,  by  placing  them  so 


320 


PHYSIOLOGIC   OPTICS 


that  the  distance  between  the  centers  of  the  two  glasses  is  greater  than 
the  distance  between  the  eyes. 


Fig.  189.  —  Stereoscope  of  Wheatstone. 

d.  When  the  image  represents  an  object  which  is  symmetrical  in  rela- 
tion to  the  median  plane,  the  two  drawings  are  symmetrical.  We  can, 

therefore,  in  this  case  obtain  a  stere- 
oscopic effect  by  looking  with  one 
eye  at  an  ordinary  drawing,  with  the 
other  at  its  image  by  reflection,  since 
the  reflection  produces  a  symmetrical 
image  of  it.  The  most  convenient 
way  is  to  look  through  a  prism  with 
total  reflection. 

e.  Placing  a  prism  with  total  reflec- 
tion in  front  of  each  eye,  we  obtain 
pseudoscopic  relief  when  we  look  at 
any  object,  providing  such  an  inter- 
pretation is  possible.  A  cigar  is  thus 
presented  as  a  hollow  leaf  of  tobacco, 
etc.  Wheatstone  had  constructed  an  instrument  of  this  kind  named 
pseudoscope  (fig.  190). 

f.  The  telestereoscope  of  Helmholtz  is  composed  of  four  mirrors  ar- 
ranged as  we  see  in  figure  191.  The  rays  ab,  a'b',  coming  from  a 
landscape,  are  reflected  by  the  large  mirrors  towards  the  small  ones,  and 
by  the  latter  towards  the  eyes.  We  obtain  the  same  effect  as  if  the  eyes 
A  and  B  were  in  the  position  of  their  images  (A±  Bx)  produced  by  the 
double  reflection.  We  have  seen  that  binocular  relief  is  due  to  the  dis- 


Fig.  190.  —  Pseudoscope  of  Wheatstone. 


BINOCULAR  PERCEPTION  OF  DEPTH 


321 


tance  which  separates  the  two  eyes.  The  greater  this  distance  is  the 
more  pronounced  is  the  relief.  The  instrument  gives  relief  to  objects 
which,  under  ordinary  circumstances,  are  too  distant  to  give  this  per- 


Fig.  191.  —  Telestereoscope  of  Helmholtz. 

ception;  at  the  same  time  it  makes  them  appear  nearer  and  smaller, 
almost  as  if  we  looked  at  a  diminished  model  of  them. 

g.  The  iconoscope  of  Javal  resembles  somewhat  an  inverted  telestere- 
oscope,  the  eyes  having  taken  the  place  of  the  object  (a  and  aj,  and  the 
object  that  of  the  eyes  (in  the  direction  of  AB). 

The  instrument  acts  as  if  the  eyes  were  very  near  each  other,  at  c 
and  q.  Looking  at  objects  through  this  instrument,  the  relief  disap- 
pears :  the  object  appears  flat,  as  in  a  painting.  On  the  contrary,  if  we 
observe  an  engraving  through  the  instrument,  it  presents  a  more  pro- 
nounced relief  than  under  ordinary  circumstances.  For,  the  binocular 
vision  then  ceases  to  make  us  observe  that  the  different  parts  of  the 
image  are  in  the  same  plane,  which  destroys  the  illusion.  Looking 
through  the  iconoscope  the  relief  is  more  marked  than  when  simply 
closing  one  eye. 

h.  The  binocular  ophthalmoscope  of  Giraud-Teulon  is  analogous  to 
the  iconoscope.  The  mirrors  are  replaced  by  two  glass  rhombohedra, 
each  of  which  covers  half  of  the  opening  of  the  ophthalmoscope.  As 


322 


PHYSIOLOGIC  OPTICS 


in  the  preceding  case,  the  rays  reach  the  eye  after  a  double  reflection  on 
the  small  surfaces  of  the  rhombohedron.  The  instrument  acts  as  if  the 
eyes  were  at  cc±  (fig.  192). 

i.  We  draw  the  two  figures,  over  each  other,  one  with  red  lines,  the 
other  with  blue  lines.  Looking  through  a  red  glass  we  do  not  see  the 
red  lines,  and  vice  versa.  —  If  we  look  at  these  anaglyphs,  placing  a  red 


Fig.  192.  —  Binocular  ophthalmoscope  of  Giraud-Teulon. 

glass  in  front  of  one  eye  and  a  blue  glass  in  front  of  the  other,  we  ob- 
tain a  stereoscopic  effect.  Changing  the  glasses  the  relief  is  reversed, 
if  the  nature  of  the  object  permits  such  an  interpretation  (d* Almeida). 


132.  The  effect  of  the  stereoscope  is  to  give  an  idea  of  the  third  dimen- 
sion, such  as  no  other  representation  can  give  of  it.  Its  use  has  become 
especially  popular  since  stereoscopic  photographs  have  been  made,  for 
though  we  can  make  stereoscopic  drawings  of  stereometric  figures,  etc., 
it  is  impossible  to  make  them  of  a  landscape  so  that  the  reproduction 
may  be  exact.  Dove  used  the  stereoscope  to  see  whether  a  bank  note 
was  false,  by  placing  it  in  one  of  the  fields  and  putting  a  genuine  note 
in  the  other.  If  it  was  false  he  saw  some  of  the  letters  leave  the  plane 
of  the  paper,  for  it  is  impossible  to  make  an  entirely  exact  counterfeit 
of  an  engraving,  and  the  least  difference  in  the  distance  of  the  letters 
produces  relief. 

STEREOSCOPIC  LUSTRE.  —  Under  ordinary  circumstances  there  are 
usually  formed  only  in  one  eye  images  of  the  same  objects  as  in  the 


BINOCULAR  PERCEPTION  OF  DEPTH  323 

other ;  as  long  as  we  place  in  the  stereoscope  images  of  real  objects  only, 
we  simply  see  the  relief.  I  have  already  said  that,  in  the  case  of  the 
controlled  reading  of  Javal,  we  see  at  the  same  place  the  stick  and  the 
letters  which  it  should  conceal.  The  observer  gets  over  the  difficulty 
by  supposing  the  stick  transparent.  Another  interpretation  of  the  same 
kind  is  known  as  stereoscopic  lustre  (Dove).  If  we  draw  one  of  the  stereo- 
scopic figures  with  black  lines  on  a  white  ground,  the  other  with  white 
lines  on  a  black  ground,  we  observe  that  the  fused  image  presents  a 
certain  brightness,  almost  as  if  it  was  covered  with  a  layer  of  plumbago. 
Replacing  the  black  surfaces  by  colored  surfaces,  we  sometimes  obtain 
the  metallic  lustre.  —  Every  bright  body,  in  fact,  sends  back  two  kinds 
of  light :  regularly  reflected  white  light  and  diffuse  light  which  has  the 
color  of  the  body  itself.  When,  in  the  stereoscope,  we  see  at  the  same 
place  white  light  and  colored  light,  the  contradiction  is  explained  by 
supposing  that  the  object  we  look  at  is  bright. 

ANTAGONISM  OF  THE  VISUAL  FIELDS.  —  When  the  images  placed  in 
the  two  fields  are  so  different  that  they  cannot  be  fused,  as,  for  example, 
if  we  present  to  one  eye  horizontal  lines  and  to  the  other  vertical  lines,' 
we  observe  the  phenomenon  known  as  antagonism  of  the  visual  fields: 
it  is  sometimes  one,  sometimes  the  other  field  which  predominates,  and 
while  one  predominates  the  other  is  suppressed ;  we  do  not  see  it  at  all. 
It  is  not  the  field  of  the  same  eye  which  predominates  everywhere ;  the 
common  field  is  composed  of  parts  belonging  to  either  eye.  When  one 
of  the  fields  has  predominated  at  one  place  for  some  time,  the  appear- 
ance changes,  the  other  field  getting  the  upper  hand.  The  change  often 
takes  place  under  an  external  influence;  a  winking  of  the  eyelids  or  a 
change  in  the  direction  of  the  look  sometimes  suffices  to  bring  it  about. 
Furthermore,  the  phenomena  vary  much  according  to  the  objects. 

If  we  present  to  each  eye  outline  pictures  which  do  not  correspond 
to  each  other,  drawn  on  a  uniform  ground,  but  different  for  both  eyes, 
we  observe  that  the  ground  of  each  field  predominates  near  the  picture 
which  belongs  to  it.  The  following  experiment  demonstrates  this  fact 
in  a  quite  striking  manner.  We  draw  in  one  of  the  fields  a  large  black 
vertical  bar,  in  the  other,  another  similar  but  horizontal  bar:  on  blend- 
ing the  fields  the  bars  form  a  cross  (fig.  193),  the  middle  of  which, 
situated  at  the  point  where  the  two  bars  cross,  is  black ;  the  parts  next 
to  the  middle  are  whitish,  because  the  outline  picture  makes  the  white 
ground  predominate.  The  extremities  of  the  arms  appear,  on  the  con- 
trary, almost  as  black  as  the  middle,  in  spite  of  the  superimposing  of  the 
white  on  the  other  field. 


324 


PHYSIOLOGIC  OPTICS 


Fig.  193.  —After  Hdmholtz. 


In  making  this  experiment,  we  experience  a  difficulty  in  fixing  the 

images  on  each  other :  the  vertical  arm 
glides  on  the  horizontal  arm.  This  is 
due  to  the  fact  that  there  are  no  com- 
mon vertical  lines  which  can  guide  us 
for  the  degree  of  convergence.  On 
account  of  their  importance  for  con- 
vergence we  designate  the  vertical 
lines  as  the  dominating  outlines.  To 
prevent  the  two  figures  from  gliding 
on  each  other,  we  place  at  the  middle 
of  each  line  a  small  white  cross.  The 
tendency  to  fuse  these  small  crosses 
suffices  to  fix  the  vertical  bar  at  the 
middle  of  the  horizontal  bar. 

When  the  two  fields  have  not  the  same  color,  we  generally  observe 
antagonism  of  the  visual  fields.  I  have  thus  arranged  the  experiment 
,with  colored  shadows  (page  240)  so  as  to  have  one  of  the  shadows  in 
each  field  of  the  stereoscope.  On  blending  them  it  was  sometimes  one, 
sometimes  the  other  color  which  predominated.  I  repeated  the  experi- 
ment with  several  of  my  pupils,  none  of  whom  succeeded  in  seeing  the 
gray  shadow.  —  There  are  authors,  however,  who  claim  to  have  ob- 
tained the  color  of  the  mixture ;  the  phenomenon  is  then,  perhaps,  of  the 
same  order  as  stereoscopic  lustre. 

133.  Identical  Points  of  the  Retinae.  —  We  say  that  one  point  of  a 
retina  is  corresponding  to,  or  identical  with,  a  point  of  the  other  one, 
when  the  images  of  the  same  exterior  point  falling  on  these  two  retinal 
points  are  blended  into  a  single  image.  If,  in  the  second  eye,  the  image 
is  formed  on  any  other  point,  it  is  not  blended  with  that  of  the  first  eye : 
the  point  is  seen  double. 

It  is  evident  that  the  two  foveas  are  corresponding  points,  since  the 
object  fixed  is  always  single.  To  find  the  other  identical  points,  Johannes 
Muller  has  given  the  following  rule.  We  suppose  the  retina  divided 
into  quadrants  by  a  horizontal  meridian  and  a  vertical  meridian,  both 
passing  through  the  fovea.  The  position  of  each  point  is  then  deter- 
mined, as  on  a  terrestrial  globe,  by  its  longitude  and  latitude  in  rela- 
tion to  these  two  meridians.  Two  points  having  the  same  longitude  and 
latitude  are  identical.  The  rule  of  Muller  agrees  with  that  which  we 
have  laid  down  in  chapter  XXI,  according  to  which  an  object  is  seen 


BINOCULAR  PERCEPTION  OF  DEPTH  325 

single  when  the  two  eyes  see  it  in  the  same  direction  in  relation  to 
the  point  fixed. 

The  researches  of  Volkmann  have  shown  that  the  law  of  Miiller  is  not 
wholly  exact,  and  that  it  is  necessary  to  replace  the  vertical  meridians 
by  apparently  vertical  meridians,  which,  for  a  person  standing  upright 
and  looking  towards  the  horizon,  converge  about  two  degrees  in  the 
downward  direction,  so  as  to  almost  meet  at  the  ground  (see  page  295). 
We  then  suppose  the  retina  divided  by  circles  parallel  to  this  meridian 
as  well  as  to  the  horizontal  meridian,  and  the  law  of  Miiller  is  applic- 
able. —  Placing  in  each  field  a  really  vertical  line,  these  lines  appear  to 
converge  upwards  and  must,  consequently,  cross  if  we  try  to  blend 
them.  In  order  that  the  experiment  may  succeed  it  is  necessary,  how- 
ever, to  arrange  them  so  that  one  line  may  be  white  on  a  black  ground, 
the  other  black  on  a  white  ground.  Otherwise  the  lines  are  blended 
nevertheless. 

THEORIES  ON  THE  NATURE  OF  IDENTITY.  —  The  question  of  knowing 
why  two  points  are  corresponding  while  two  others  are  not,  has  been 
much  discussed.  Most  of  the  advocates  of  the  theory  of  identity  suppose 
that  there  exists  an  anatomical  relation  between  the  two  corresponding 
points.  They  suppose  that  the  nerves  conducting  the  impressions  of 
two  corresponding  points  unite,  on  their  way  to  the  chiasma,  into  one 
which  conducts  the  impression  to  the  brain.  This  idea  was  already 
expressed  by  Galien,  and  has  been  confirmed  by  Newton,  Wollaston  and 
others.  The  so-called  theory  of  projections  is  expressed  almost  as  we 
have  described  it  in  chapter  XXI:  a  point  on  the  left  retina,  situated 
10  degrees  to  the  left  of  the  fovea,  localizes  its  impression  at  10  degrees 
to  the  right  of  the  point  of  fixation ;  the  point  situated  at  10  degrees  to 
the  left  of  the  right  fovea  localizes  its  impression  in  the  same  direction ; 
and  as  the  two  impressions  are  localized  in  the  same  direction,  they  are 
blended  into  one.  The  identity  of  the  two  foveas  might  be  a  result 
acquired  by  experience.  This  theory  has  been  upheld  by  Kepler,  Porter- 
Held  and,  under  an  erroneous  form,  by  Giraud-Teulon. 

Immediately  after  the  invention  of  the  stereoscope  and  the  studies 
of  the  production  of  relief  to  which  this  invention  gave  rise,  there  was 
an  inclination  to  abandon  the  idea  of  corresponding  points,  for  the 
stereoscopic  experiments  seem  opposed  to  what  we  have  said  on  these 
points.  Indeed,  let  us  look  in  the  stereoscope  at  a  representation  of 
the  two  points  A  and  B,  both  situated  in  the  median  plane,  and  fix  the 
more  distant  A.  The  images  of  B  are  not  formed  on  two  correspond- 
ing points,  since  in  one  eye  its  image  is  to  the  right,  in  the  other  to  the 


326  PHYSIOLOGIC   OPTICS 

left  of  the  fovca.  Nevertheless,  we  see  it  single  and  in  relief ;  that  is  to 
say,  nearer  than  A.  —  On  account  of  this  apparent  contradiction, 
Wheatstone  inclined  towards  the  theory  of  projections.  In  despair  of  a 
better  explanation,  the  advocates  of  the  theory  of  identity  supposed  that 
a  point  of  one  of  the  retinae  does  not  correspond  to  a  point,  but  to  a 
small  surface  of  the  other  (Panum).  An  image  falling  on  the  point  of 
the  first  retina  could  then  become  blended,  either  without  relief,  with 
an  image  formed  at  the  middle  of  the  small  surface  of  the  other,  or  with 
relief,  with  an  image  formed  on  a  more  peripheral  point  of  the  small 
surface.  But,  under  this  form,  the  theory  of  identity  was  not  tenable ; 
it  would  be  necessary,  indeed,  to  suppose  that  the  same  two  points 
could  be  sometimes  corresponding,  sometimes  not  corresponding,  which 
is  scarcely  admissible.  The  question  was  cleared  up  only  by  the  labors 
of  I  aval. 

THEORY  OF  JAVAL  ON  THE  PRODUCTION  OF  RELIEF. — This  theory  calls 
especially  for  two  factors,  the  neutralization  (partial  suppression  of  one 
of  the  images)  and  the  influence  of  the  ocular  movements,  on  which  Brucke 
had  already  insisted.  In  chapter  XXI  reference  was  made  to  the  suppres- 
sion of  one  of  the  images,  which  takes  place  when  different  images  are 
formed  on  two  corresponding  parts  of  the  retinae.  We  then  see,  some- 
times the  image  of  one  eye,  sometimes  that  of  the  other,  and  while  we 
see  the  image  of  one  eye,  the  corresponding  part  of  the  image  of  the 
other  disappears  absolutely.  In  normal  persons  the  suppression  espe- 
cially manifests  itself  alternately  for  both  eyes,  under  the  form  of  an- 
tagonism of  the  visual  fields;  in  strabismic  patients,  on  the  contrary,  we 
often  have  occasion  to  observe  the  constant  neutralization  of  a  great 
part  of  the  visual  field  of  one  eye. 

Brucke  was  the  first  who  insisted  on  the  great  importance  of  the 
ocular  movements  for  the  perception  of  relief.  Anyhow,  it  is  certain 
that  without  them  we  could  have  only  a  very  vague  notion  of  it.  Look- 
ing into  a  stereoscope,  especially  if  the  images  are  difficult  to  fuse,  it  is 
only  after  I  have  permitted  my  look  to  wander  for  some  time  on  the 
figures,  fusing  sometimes  the  images  of  the  distant  objects,  sometimes 
those  of  the  near  objects,  that  relief  appears  to  me.  As  long  as  the 
sensation  of  relief  is  not  produced  I  see  double,  sometimes  the  near 
objects,  sometimes  the  distant  ones;  but  at  the  moment  when  relief 
appears,  I  see  all  of  them  single.  Certain  authors  claim  that  they  have 
observed  relief  by  illuminating  the  stereoscopic  images  with  an  electric 
spark,  the  duration  of  which  light  is  so  short  that  all  ocular  motion  is 
necessarily  excluded.  This  would  certainly  be  impossible  in  my  case. 


BINOCULAR  PERCEPTION  OF  DEPTH 


327 


for  there  always  elapses  a  certain  time  before  the  real  illusion,  which 
does  not  prevent  me  from  being  able  to  form  all  at  once  a  vague  notion 
of  relief. 

According  to  Javal,  it  is  necessary,  indeed,  to  distinguish  between  the 
idea  of  relief,  which  is  produced  by  the  fact  that  we  see  near  objects  in 
double  crossed  images,  and  the  measurement  of  relief,  which  depends  on 
the  sensation  of  the  degree  of  innervation  necessary  to  converge  towards 
the  near  object.  To  account  for  the  manner  in  which  we  come  to  obtain 
the  sensation  of  relief,  it  is  preferable  to  use  images  which  are  quite 
difficult  to  blend,  the  stereoscopic  parallax  of  the  objects  represented 
being  quite  strong.  We  immediately  fuse  the  images  of  distant  objects, 
and  all  the  others  appear  in  double  images.  We  then  allow  the  look  to 
stray  on  the  figure,  which  forces  convergence  more  or  less,  according 
as  the  object  is  represented  more  or  less  distant.  After  having  con- 
tinued thus  for  some  time,  relief  manifests  itself  almost  in  the  same  way 
as  we  can  with  closed  eyes  obtain  a  very  distinct  idea  of  the  form  of 
an  object  by  feeling  it  with  the  fingers.  At 
the  same  time  that  relief  appears,  the  double 
images  disappear ;  the  image  of  one  or  other 
eye  is  suppressed.  If  one  of  the  eyes  plays 
the  part  of  the  directing  eye  (see  page  308)  it 
is  usually  the  images  of  the  other  eye  which 
are  suppressed,  unless  the  image  of  the  pre- 
ponderating eye  is  much  more  peripheral 
than  that  of  the  other.  In  cases  in  which 
this  preponderance  is  not  developed,  the 
double  images  seem  to  appear  following  the 
law  of  Javal:  we  suppress  that  one  of  the 
images  which  occupies  the  smallest  retinal 
surface.  We  can  account  for  the  manner  in 
which  we  suppress  the  images  by  looking  at 
a  rule  which  is  held  obliquely  before  the 
eyes,  so  that  it  presents  a  greater  surface 
to  one  eye  than  to  the  other.  Whether  it 
occupies  the  position  AA  (fig.  194),  or  the  position  BB,  it  seems  to  me, 
seen  binocularly,  to  have  the  same  appearance  as  when  I  close  the  left 
eye.  Persons  in  whom  the  preponderance  of  one  eye  is  not  developed 
see  the  rule  binocularly,  as  it  is  presented  to  the  left  eye,  if  it  occupies 
the  position  AA.  In  the  position  BB  they  see  it,  on  the  contrary,  as  it 
presents  itself  to  the  right  eye. 


Fig.  194. 


328  PHYSIOLOGIC  OPTICS 

The  discussion  of  the  two  theories  of  binocular  vision,  that  of  identity 
and  that  of  projections,  has  not  yet  closed.  The  explanation  of  Javal  is 
applicable  in  reality  as  well  to  one  as  to  the  other.  We  can  imagine  the 
projection  learned  by  experience;  and  even  the  fact  of  always  project- 
ing the  images  of  the  two  foveas  at  the  same  place,  the  foundation  stone 
of  binocular  vision,  may  be  something  learned.  It  is,  perhaps,  the 
superiority  of  the  fovea,  as  to  visual  acuity,  which  causes  us  to  always 
bring  the  images  of  the  object  which  interests  us  to  form  themselves 
on  both  foveas,  and  we  may  thus  have  been  led  to  always  localize  the 
impression  of  the  two  foveas  at  the  same  place.  On  the  other  hand, 
the  advocates  of  the  theory  of  identity  take  their  stand  on  the  anatomical 
observations  of  the  semi-decussation  in  the  chiasma,  and  especially 
on  comparative  anatomy,  which  shows  that  in  many  animals  —  fish,  for 
example  —  whose  eyes  are  placed  so  as  not  to  have  a  common  visual 
field,  the  optic  nerves  cross  completely.  Clinical  observations  in  hemi- 
anopsia,  especially  those  of  partial  hemianopsia,  are  a  further  argument 
in  favor  of  this  theory.  The  study  of  the  vision  of  strabismic  patients, 
which  is  perhaps  the  best  means  of  deciding  the  question  finally,  shows, 
as  we  shall  see  in  the  following  chapter,  that,  in  consequence  of  a  false 
position  of  the  eyes,  there  may  be  developed  a  kind  of  correspondence 
between  two  retinal  points  which,  under  ordinary  circumstances,  are 
not  corresponding;  but  this  relation  never  assumes  the  character  of 
true  binocular  vision  with  fusion,  and  it  sometimes  suffices,  in  a  person 
who  has  squinted  since  childhood,  to  place  the  eyes  in  an  approximately 
correct  position,  in  order  that,  in  the  course  of  a  fortnight,  correct  pro- 
jection may  gain  the  upper  hand. 

Bibliography.  —  Wheatstone  (C. ) .  Contributions  to  the  Physiology  of  Vision.  On  some  Re- 
markable and  hitherto  Unobserved  Phenomena  of  Binocular  Vision.  Phil,  trans.,  1838,  II,  p.  371- 
394.  —  Wheatstone  (C.).  Contributions  to  the  Physiology  of  Vision,  II.  Phil.  Mag.,  4,  III,  p. 
149-152,  and  p.  504-523.  -—  Brewster  (D.).  The  stereoscope.  London,  1858.  —  Helmholtz 
(H.).  Das  Telestereoskop.  Pogg.  Ann.,  CI,  p.  494-CII,  p.  167.  —  Javal  (E.).  Sur  un  instru- 
ment nomme  Iconoscope,  destine  d,  donner  du  relief  aux  images  planes  examinees  avec  les  deux  yeux. 
Report,  LXIII,  927.  —  Javal  (E.).  De  la  neutralisation  dans  Facte  de  la  vision.  Ann.  d'oc., 
LIV,  p.  5.  —  Miiller  (Johannes).  Beitrage  zur  vergleichende  Physiologic  des  Gesitchtssinnes. 
Leipzig,  1826,  p.  191.  —  Volkmann  (A.  W.).  Physiologische  Untersuchungen  im  Gebiete  der 
Optik,  II.  Leipzig,  1864.  —  Newton  (J.).  Opticks,  1717,  p.  320.  —  Panum  (P.  L.).  Phi/si- 
ologische  Untersuchung  uber  das  Sehen  mit  zwei  Augen.  Kiel,  1858.  —  Briicke.  Ueber  die 
stereoscopische  Erscheinungen.  Miiller' s  Archiv  fur  Anat.  u.  PhysioL,  1841,  p.  459.  —  Nagel 
(A.).  -Dos  Sehen  mit  zwei  Augen  und  die  Lehrevonden  identischen  Netzhautstellen.  Leipzig, 
1861.  —  Javal  (E.).  Manuel  du  strabisme.  Paris,  Masson,  1896. 


CHAPTER   XXIV. 

STRABISMUS. 

134.  Different  Forms  of  Strabismus.  —  We  say  that  there  is  strabismus 
when  the  two  visual  lines  do  not  intersect  at  the  point  fixed.  The 
image  of  the  point  fixed  is  not,  therefore,  formed  on  the  two  foveas,  and 
since  the  two  foveas  are  always  corresponding  points,  there  is  no 
binocular  vision.  One  might,  therefore,  define  strabismus  as  the  con- 
dition in  which  binocular  vision  is  wanting,  at  least  at  certain  moments 
or  for  certain  directions  of  the  look.  It  must  be  observed,  however, 
that  we  may  meet  with  cases  in  which  the  visual  lines  have  the  proper 
direction,  at  least  apparently,  but  in  which  binocular  vision  is,  never- 
theless, wanting;  this  case  often  presents  itself  in  persons  affected  with 
strabismus,  who  have  undergone  a  successful  operation.  It  is  also 
customary  to  speak  of  strabismus  when  one  eye  deviates,  even  if  it  is 
completely  blind.  The  study  of  strabismic  patients  is  very  important 
for  different  questions  of  physiologic  optics. 

We  distinguish  two  forms  of  strabismus :  paralytic  strabismus,  due  to 
a  paralysis  of  one  or  more  muscles,  and  concomitant  strabismus,  which,  in 
the  great  majority  of  cases,  is  due  to  the  defect  of  innervation  (Hanscn- 
Grut).  The  symptoms  by  which  we  make  the  differential  diagnosis 
between  these  two  forms  of  strabismus  are  well  known.  They  have 
passed  from  the  classic  memoir  of  Graefe  into  all  treatises  of  ophthal- 
mology. In  cases  of  paralytic  strabismus  the  excursion  of  the  eye  is 
less  on  the  side  of  the  paralyzed  muscle,  and  the  secondary  deviation  is 
greater  than  the  primary.  Patients  present  diplopia,  either  spontane- 
ously, or  more  especially  if  we  examine  them  with  a  candle  and  a  colored 
glass.  The  distance  between  the  two  images  increases  when  the  look 
is  directed  towards  the  side  of  the  diseased  muscle,  and  it  is  the  image 
of  the  diseased  eye  which  is  farthest  away  in  this  direction. 

When  the  patient  closes  the  healthy  eye  and  looks  towards  an  object 
situated  on  the  side  of  the  diseased  muscle,  the  projection  is  false;  for, 

329 


330  PHYSIOLOGIC  OPTICS 

as  it  is  necessary,  on  account  of  the  paresis,  to  use  a  stronger  innerva- 
tion  to  bring  the  eye  to  fix  the  object,  the  patient  thinks  that  this  object 
is  situated  more  to  one  side  than  it  really  is,  and  when  he  wants  to 
grasp  it  quickly  he  brings  the  hand  too  far  to  that  side.  I  have  already 
observed  (page  305)  the  importance  of  this  observation  to  demonstrate 
that  we  judge  the  direction  of  the  look  above  all  by  the  degree  of  in- 
nervation  used  to  bring  it  into  this  direction. 

CONCOMITANT  STRABISMUS.  —  When  we  speak  of  strabismus  with- 
out other  qualification  it  is  generally  this  form  that  we  mean.  —  In  this 
strabismus  the  deviation  is  almost  the  same  for  all  directions  of  the 
look,  except  that  generally  the  convergence  is  more  pronounced  for 
the  downward  than  for  the  upward  look.  The  secondary  deviation  is 
equal  to  the  primary  deviation.  The  patient  does  not  complain  of 
diplopia,  but  we  may  always  bring  it  about  by  the  means  which  I  shall 
describe  forthwith.  The  distance  between  the  two  images  is  the  same 
everywhere,  to  whichever  side  the  patient  looks.  The  simplest  means 
of  diagnosing  strabismus  is  to  make  the  patient  fix  an  object,  the  finger 
of  the  observer,  for  example.  If  one  of  the  eyes  seems  to  deviate,  we 
cover  the  other,  and  if  the  former  then  makes  a  movement  to  fix,  it 
was  deviated :  strabismus  is,  therefore,  proved.  This  examination  must 
be  repeated  for  a  distant  object.  If  we  do  not  discover  strabismus  by 
this  means,  it  may,  nevertheless,  happen  that  the  patient  has  it,  but  in 
a  very  slight  degree,  or,  in  other  words,  that  he  has  no  binocular  vision ; 
we  may,  in  this  case,  place  a  prism,  apex  inwards,  in  front  of  the  eye. 
If  there  is  binocular  vision  the  eye  makes  a  movement  of  convergence 
to  neutralize  the  effect  of  the  prism  (Graefe).  —  If  the  strabismus  is 
periodic  we  can  sometimes  discover  it  by  making  the  patient  fix  a  very 
small  object,  a  word  printed  in  very  small  type,  for  example;  the  patient 
is  obliged  to  accommodate  to  distinguish  the  word,  and  the  effort  of 
accommodation  may  then  cause  strabismus. 

LATENT  STRABISMUS.  —  In  order  to  see  whether  there  is  latent  stra- 
bismus, we  make  the  patient  fix  the  finger  of  the  observer ;  we  cover  one 
eye  and  examine,  on  uncovering  it,  whether  the  eye  deviated  under  the 
hand  and  whether  it  straightened  itself  in  order  to  fix.  If  the  deviating 
eye  does  not  straighten  itself,  the  strabismus  has  become  manifest ;  if  it 
does  straighten  itself,  it  is  latent.  —  According  to  Graefe,  we  make  the 
patient  observe  a  long  vertical  line  which  has  at  the  middle  a  black  spot, 
or,  which  is  preferable,  a  candle,  while  we  place  in  front  of  one  of  his  eyes 
a  prism,  apex  upwards.  If  there  is  latent  strabismus,  the  patient  sees 
two  objects  placed  exactly  one  above  the  other  (if  the  apex  of  the  prism 


STRABISMUS  331 

forms  a  horizontal  line).  If  not,  there  is  latent  strabismus,  and  we  can 
then  measure  the  degree  of  it  by  placing  the  prism  of  Cretes  before  the 
other  eye  and  finding  the  degree  of  this  prism  which  makes  one  image 
appear  above  the  other.  We  can  also  use  the  Maddox  test,  etc.  Javal 
placed  a  ground  glass  lens  before  one  of  the  eyes  of  the  patient;  this 
glass  prevents  the  eye  which  it  covers  from  distinguishing  anything, 
while  the  observing  eye  sees  the  covered  eye  sufficiently  well  to  judge 
of  its  position. 

Making  the  examination  in  this  way,  we  find,  in  many  people,  a  slight 
degree  of  latent  divergent  strabismus  for  near  vision.  This  condition 
is  often  designated  as  insufficiency  of  the  internal  recti.  This  expression 
is  ill-chosen  and  should  be  discontinued.  The  internal  recti  are  not 
weaker  than  in  the  normal  eyes,  as  Hansen-Grut  has  shown,  for,  other- 
wise this  weakness  ought  to  manifest  itself  also  for  the  associated  move- 
ments. If  the  right  internal  rectus  were  really  weaker  than  in  the  normal 
state,  we  should,  when  looking  to  the  left,  see  the  phenomena  appear 
which  characterize  paresis  of  the  right  internal  rectus,  which  is  by  no 
means  the  case.  It  is  not  in  the  muscles,  it  is  in  the  innervation  of 
convergence  that  we  must  search  for  the  cause  of  this  deviation.  We 
might,  therefore,  speak  of  an  insufficiency  of  convergence,  but  this  also 
would  be  a  bad  expression,  for  many  patients  affected  with  this  defi- 
ciency can  converge  as  well  as  normal  persons ;  it  is  only  the  stimulus 
of  convergence  that  is  wanting,  (i) 

135.  Measurement  of  Strabismus.  —  i°  We  cover  the  good  eye;  the 
strabismic  eye  straightens  itself,  and  we  value,  in  millimeters,  the  extent 
of  the  displacement  of  the  cornea. 

2°  Javal  has  proposed  to  measure  the  deviation  in  degrees  by  means 
of  the  perimeter.  He  places  the  patient  so  that  the  strabismic  eye  is 
in  front  of  the  point  of  fixation  of  the  perimeter.  The  patient  fixes  this 
point  with  his  good  eye.  The  observer  then  moves  a  candle  along  the 
arc  of  the  perimeter,  sighting  in  the  direction  of  this  candle  towards  the 
strabismic  angle.  He  finds  the  position  in  which  the  corneal  image  is 
at  the  middle  of  the  pupil,  which  indicates  approximately  the  direction 
of  the  visual  line  of  the  strabismic  eye.  In  the  keratoscopic  arc  of  de 
Wecker,  the  candle  is  replaced  by  a  white  mire,  and  at  the  point  of  fixa- 
tion is  a  small  mirror  in  which  is  reflected  a  distant  object  which  serves 
as  the  point  of  fixation. 


(1)  [In  this  country  Stevens'  nomenclature  has  been  generally  accepted.    According  to  him  this  con 
dltion  is  called  exoph&ria.]—W. 


332  PHYSIOLOGIC  OPTICS 

3°  We  can  use  the  distance  of  the  two  images  as  a  measure  of  the 
strabismus  if  there  is  diplopia.  We  can  measure  this  distance  with  the 
prism  of  Cretes,  or  by  projecting  the  images  on  a  wall  provided  with  a 
graduation  in  degrees  (Hirschberg,  Landolf)  or  on  a  Prentice  scale. 

The  deviation  often  varies  much  with  the  distance  of  the  object  fixed. 
It  may  also  be  useful  to  determine  the  deviation  at  different  distances, 
at  4  meters  and  at  25  centimeters,  for  example,  as  Schioetz  has  proposed. 

136.  The  etiology  of  concomitant  strabismus  is  a  quite  complex  ques- 
tion on  which  opinions  are  still  divided.  Boehm  discovered  the  relation 
which  exists  between  hypermetropia  and  convergent  strabismus,  and 
Bonders,  in  a  general  way,  announced  the  part  that  the  anomalies  of 
re-fraction  play  in  the  etiology  of  strabismus.  This  influence  cannot  be 
denied,  and  it  is  especially  striking  for  convergent  strabismus.  In  my 
extensive  compilation  of  statistics  of  young  conscripts  (see  page  84) 
there  were  42  cases  of  convergent  strabismus,  of  whom  31  were  hyper- 
metropes,  7  emmetropes  and  4  myopes ;  that  is  to  say,  that  about  70  per 
cent,  of  the  persons  squinting  inwards  were  hypermetropes.  But,  on 
the  other  hand,  there  were  in  all  301  hypermetropes  (of  2  dioptrics  or 
more) ;  only  a  very  small  minority  of  the  hypermetropes  squint,  there- 
fore. 

The  manner  in  which  Bonders  explained  the  relation  between  con- 
vergent strabismus  and  hypermetropia  is  well  known.  When  an  emme- 
trope  fixes  a  near  object,  it  is  above  all  the  necessity  of  seeing  it  single 
which  regulates  the  position  of  his  eyes.  But,  if  we  cover  one  of  the 
eyes,  this  need  no  longer  exists,  and,  nevertheless,  the  observed  person 
generally  continues  to  converge  towards  the  point  fixed;  this  is  due 
to  the  relationship  which  exists  between  accommodation  and  converg- 
ence. Even  if  the  observed  person  is  sufficiently  myopic  to  make  it  un- 
necessary for  him  to  accommodate  for  the  object,  the  covered  eye  con- 
verges, nevertheless,  pretty  exactly  for  the  object.  This  is  due  to  what 
Hansen-Grut  termed  sensation  of  the  distance;  knowing  that  the  object  is 
at  a  short  distance  away,  the  patient  converges  because  he  is  accustomed 
to  do  so  in  the  interest  of  binocular  vision,  even  in  a  case  in  which  this 
interest  no  longer  exists. 

These  three  factors  regulate  the  degree  of  convergence  to  be  used. 
Under  ordinary  circumstances,  it  is  the  first  factor  which  is  of  most 
importance ;  but,  in  cases  of  hypermetropia,  it  may  happen  that,  in  order 
to  sustain  his  accommodation,  the  patient  converges  more  than  is  neces- 
sary for  fusion.  He  then  sacrifices  his  binocular  vision  to  obtain  distinct 
vision  with  one  eye  only,  and  this  happens  with  special  ease  when  the 


STRABISMUS  333 

vision  of  the  other  eye  is  diminished  for  one  reason  or  another  (opacities 
of  the  cornea,  astigmatism,  etc.).  In  a  certain  number  of  cases  we  find 
vision  greatly  diminished  without  any  perceptible  reason.  We  cannot 
yet  say  whether  this  diminution  is  a  consequence  of  strabismus  (ambly- 
opia  ex  anopsid),  or  whether  it  is  not  rather  a  cause  of  strabismus,  due  to 
a  congenital  anomaly. 

If  we  thus  explain  why  a  hypermetrope  may  become  strabismic,  we 
cannot  well  understand  why  the  great  majority  of  hypermetropes  do  not 
squint.  They  often  seem  to  have  quite  as  much  reason  to  squint  as 
strabismic  patients.  Javal  supposes  that  strabismus  has  developed  under 
the  influence  of  paresis  of  the  accommodation  which  is  cured  later. 
The  existence  of  such  paresis  is  certainly  hypothetical,  but  it  would  very 
well  explain  the  origin  of  strabismus ;  the  parents  of  strabismic  children 
are  quite  frequently  affected  with  convulsions,  intestinal  worms,  which 
might  have  produced  nervous  troubles,  etc.  According  to  de  Wecker, 
a  certain  number  of  cases  of  convergent  strabismus  might  be  due  to  a 
paralysis  of  one  of  the  external  recti  acquired  during  infancy.  Paralytic 
strabismus  would  be  transformed  later  into  concomitant  strabismus. 

Myopia  plays,  in  the  production  of  divergent  strabismus,  a  less  im- 
portant role  than  hypermetropia  in  the  production  of  convergent  stra- 
bismus. As  the  myope  does  not  accommodate  at  all,  or  only  slightly 
for  near  objects,  one  of  the  factors  which  sustains  convergence  is  want- 
ing. If  the  eyes  are  very  unequal,  there  may  readily  follow  a  divergent 
strabismus  relative  to  near  objects.  On  the  other  hand,  distant  vision 
is  so  diffuse  for  the  more  imperfect  eye  that  binocular  vision  is  of  little 
usefulness,  and  this  eye  then  easily  deviates  outwards.  Generally  speak- 
ing, every  eye,  the  vision  of  which  is  destroyed  or  greatly  diminished, 
has  a  tendency  to  deviate  outwards.  —  In  very  rare  cases  we  meet  in 
myopes  a  special  form  of  convergent  strabismus. 

The  ideas  on  the  nature  of  strabismus  are  much  divided.  Most  authors 
find  the  cause  of  strabismus  in  the  muscles,  for  instance,  v.  Graefe  ("ex- 
cess of  average  contraction"),  Schweigger  ("excess  of  elasticity  of  the 
muscles"),  etc.  Others,  Alfred  Graefe  and  Javal,  for  instance,  attribute 
periodic  strabismus  and  the  variable  part  of  permanent  strabismus  to 
innervation,  while  they  suppose  that  the  permanent  part  is  dua  to  con- 
secutive muscular  alterations.  The  theories  which  attribute  the  vast 
majority  of  cases  of  strabismus  to  a  defect  of  innervation  are  beginning 
to  gain  ground.  They  have  been  advocated  by  Stellwag,  Rdhlmann, 
Hansen-Grut  and  Parinaud.  The  theory  of  Hansen-Grut  seems  to  me  to 
adapt  itself  best  to  the  phenomena. 


334  PHYSIOLOGIC   OPTICS 

According  to  this  author,  the  whole  muscular  theory  collapses  before 
the  following  observation.  Suppose  a  left  convergent  strabismus  of 
6  mm. :  if  this  strabismus  had  a  muscular  origin,  it  would  be  necessary 
that  the  limit  of  excursion  outwards  of  the  left  eye  would  be  displaced 
inwards  6  mm.  But  we  never  find  anything  of  the  kind.  If  the  limit 
is  sometimes  displaced  a  little  inwards,  this  is  due  to  a  lack  of  habit, 
since  we  never  have  occasion  to  make  so  great  a  motion  with  the  stra- 
bismic  eye. 

Hansen-Grut  distinguishes  between  the  position  of  anatomic  equilibrium 
and  the  position  of  functional  equilibrium  of  the  eyes.  The  former  is  the 
position  which  the  eyes  assume  apart  from  all  nervous  influence.  When 
the  eyes  are  in  this  position  (during  sleep,  after  death,  etc.),  the  visual 
lines  diverge  in  nearly  all  patients.  The  position  of  functional  equilibrium 
is  the  position  which  the  eyes  assume  when  we  look  at  a  distant  object 
with  one  eye  covered.  In  this  position  the  visual  lines  are  parallel  in 
normal  persons.  The  convergent  strabismus  is  due  to  the  fact  that 
there  is  developed  an  unusual  position  of  functional  equilibrium ;  the 
divergent  strabismus,  on  the  contrary,  is  due  to  the  fact  that  such  a 
position  is  not  developed  at  all,  so  that  the  eyes  are  placed  in  the  posi- 
tion of  anatomic  equilibrium. 

137.  Vision  of  Strabismic  Patients.  —  Except  in  cases  of  convergent 
strabismus  of  myopes,  strabismic  patients  do  not  generally  complain  of 
diplopia;  they  suppress  the  image  of  the  deviated  eye,  so  that  the  stra- 
bismic eye  serves  only  to  slightly  increase  the  visual  field.  We  may, 
however,  always  cause  diplopia  by  holding  a  red  glass  in  front  of  the 
good  eye,  by  keeping  this  eye  closed  for  some  days,  etc. ;  but  then  we 
often  meet  with  the  singular  phenomenon  termed  paradoxical  diplopia. 
This  diplopia  was  discovered  by  v.  Graefe.  Examining  persons  affected 
with  convergent  strabismus,  in  whom  he  had  performed  a  tenotomy 
which  partly  corrected  the  defect,  he  found  crossed  diplopia,  although 
the  visual  lines  were  still  convergent,  and  the  patients,  according  to  the 
ordinary  rule,  should  have  indicated  homonymous  diplopia.  Javal  was 
the  first  to  study  this  phenomenon  on  patients  not  operated  on.  The  ex- 
planation of  this  fact  is  that  there  is  developed  what  has  been  very  im- 
properly named  a  vicarious  fovea.  The  patient  has  first  cultivated  the 
habit  of  suppressing  the  image  of  the  strabismic  eye ;  then  there  is  gradu- 
ally formed  an  idea  of  the  false  position  of  the  strabismic  eye ;  he  has 
learned  that  an  object  which  forms  its  image  on  the  fovea  of  the  good  eye, 
forms  its  image  at  a  point  (b)  inwards  from  the  fovea  of  the  strabismic 


STRABISMUS  335 

eye,  and  he  has  learned  to  localize  this  image  at  the  place  where  the  ob- 
ject to  which  it  belongs  is  situated.  If  we  place  a  prism,  apex  down,  in 
front  of  the  good  eye,  the  patient  sometimes  says  that  he  sees  only  the 
image  of  this  eye,  but  generally  we  succeed  in  making  him  see  also  the 
image  of  the  strabismic  eye ;  the  patients  localize  it  almost  on  the  same 
vertical  line  as  the  image  of  the  good  eye,  instead  of  indicating  widely 
separate  homonymous  images.  It  is,  therefore,  as  if  there  was  developed 
a  correspondence  between  the  point  b  and  the  fovea  of  the  good  eye.  But 
the  localization  of  the  image  is  always  very  uncertain ;  the  patient  some- 
times says  that  he  sees  both  images  well,  but  that  it  is  impossible  to 
tell  which  is  the  image  of  the  strabismic  eye. 

If  we  perform  a  tenotomy  which  does  not  completely  correct  the 
deviation,  the  image  of  the  point  fixed  is  no  longer  formed  either  on 
the  true  fovea  or  the  vicarious  fovea,  but  between  the  two.  Patients 
first  project  the  image  according  to  the  vicarious  fovea:  as  it  is  formed 
on  a  part  of  the  retina  situated  outside  of  the  latter,  the  patient  sees  the 
object  in  crossed  images.  Later,  especially  if  we  make  systematic  exer- 
cises in  order  to  reach  it,  the  true  fovea  comes  to  exert  its  preponderat- 
ing influence :  the  patient  sees  the  object  in  homonymous  images.  Fol- 
lowing the  development  of  the  change  of  vision  of  the  patient,  we  some- 
times succeed  in  finding  a  time  when  the  patient  projects  the  image  of 
the  strabismic  eye  according  to  both  foveas  at  once:  he  sees  with  the 
strabismic  eye,  at  the  same  time,  one  image  to  the  right  and  another 
to  the  left  of  the  object.  This  singular  form  of  vision  has  been  described 
by  Javal  under  the  name  binocular  triplopia.  I  have  had  occasion  to 
study  a  case  of  this  character. 

138.  Treatment  of  Strabismus.  —  If  we  confine  ourselves  to  the  treat- 
ment by  operation,  it  is  prudent  not  to  completely  correct  convergent 
strabismus,  for  the  strabismic  eye  has  a  tendency  to  put  itself  in  diverg- 
ence, a  tendency  which  sometimes  suffices  by  itself  to  finally  cause  the 
convergent  strabismus  to  disappear.  On  the  contrary,  when  it  is  our  in- 
tention to  reestablish  binocular  vision,  we  must  try  to  make  the  position 
of  the  eyes  as  correct  as  possible.  This  reestablishment  is  often  a  very 
long  and  difficult  matter ;  the  task  is  less  arduous  in  cases  in  which  there 
still  exists  binocular  vision  in  a  part  of  the  field.  In  certain  cases, 
such  as  the  periodical  divergent  strabismus  and  the  convergent  stra- 
bismus of  myopes,  we  succeed  by  means  of  some  exercises,  or  even  by 
the  simple  operative  treatment.  According  to  Javal,  who  especially  de- 
voted his  attention  to  this  question,  the  course  of  the  treatment  is  as 
follows : 


336  PHYSIOLOGIC  OPTICS 

a.  Reestablishment  of  diplopia  and,  if  possible,  of  the  vision  of  the  stra- 
bismic  eye.    We  keep  the  good  eye  covered  by  means  of  a  blind  patch ; 
if  the  vision  of  the  other  eye  is  very  bad,  in  order  to  less  annoy  the 
patient,  we  allow  him  to  wear  the  patch  on  the  bad  eye  during  several 
hours  of  the  day;  but  it  is  necessary,  during  this  period  of  treatment, 
never  to  allow  the  two  eyes  to  be  uncovered  at  the  same  time,  under 
penalty  of  never  seeing  the  neutralization  disappear  or  of  seeing  the 
strabismus  increase;  for,  as  the  diplopia  annoys  so  much  less  as  the 
images  are  more  distant  from  each  other,  the  patient  tries  to  squint 
more  strongly  in  order  to  separate  the  images. 

b.  Reestablishment  of  the  approximately  correct  position  of  the  eyes  by 
way  of  operation. 

c.  Stereoscopic  exercises.  —  We  begin  by  placing  in  each  field,  on  each 
visual  line,  a  round  spot.     If  the  patient  fuses  them,  we  move  them 
farther  or  nearer,  in  order  to  develop  in  him  the  necessity  of  seeing 
single.    The  stereoscope  of  Javal,  an  imitation  of  that  of  Wheatstone  (fig. 
189),  but  with  a  variable  angle  between  the  mirrors,  lends  itself  very 
well  to  this  exercise.    As  soon  as  the  patient  sees  double,  we  begin. 
When  the  patient  has  succeeded,  we  make  him  fuse  letters  by  giving 
him  smaller  and  smaller  characters.    For  all  these  tests  it  is  necessary 
to  add  to  each  figure  numerous  small  marks,  different  ones  for  each 
eye,  in  order  to  make  certain  that  the  patient  really  fuses.    He  ought  to 
see  the  figure  with  both  series  of  marks ;  otherwise,  he  neutralizes  one 
of  the  figures,  instead  of  fusing  both.    When  beginning  these  exercises, 
we  often  encounter  the  phenomenon  which  v.  Graefe  designated  under 
the  name  of  antipathy  to  single  vision.    When  we  place  the  round  spots 
in  positions  corresponding  to  the  visual  lines,  the  patient  converges  or 
diverges  in  order  not  to  fuse  them;  if  we  try,  in  this  new  position  of 
the  eyes,  he  makes  his  convergence  change  again,  and  so  forth.    Javal 
invented  a  very  ingenious  card  to  surmount  this  difficulty,  which  is 
often  very  great. 

d.  Exercises  without  the  stereoscope.  —  There  often  exists  a  part  of  the 
field  in  which  the  patient  sees  single;  then  we  make  him  exercise  in 
order  to  increase  this  part,  for  example,  by  placing  a  candle  in  the  part 
of  the  field  in  which  the  patient  fuses  and  bringing  it  towards  the  other 
part;  when  the  patient  sees  double,  we  begin  again. 

e.  If  the  patient  stands  these  different  tests,  we  begin  to  make  him 
do  controlled  reading.    We  interpose  a  pencil  between  the  eyes  and  the 
book ;  reading  can  then  take  place  without  interruptions  only  by  using 
both  eyes.    This  exercise  must  be  continued  for  months.    It  is  only  a 


STRABISMUS  337 

long  while  after  the  reestablishment  of  binocular  vision  that  the  patient 
can  see  relief. 

Bibliography.  —  Bohm.  Das  Schielen.  Berlin,  1845.  —  v.  Grafe  (A.).  Ueber  Dop- 
peltxehen  nach  Schieloperationen  und  Incongruenz  derNetzhaiite.  Arch.  f.  Ophth.,  I,  1,  p.  82.  — 
v.  Grafe  (A.).  Ueber  eigenthiimliche  zur  Zeit  nock  unerkldrliche  Anomalien  in  der  Projection  der 
Netzhautbilder.  Arch.  f.  Ophth.,  II,  1,  p.  284.  —  v.  Grafe  (A.).  Symptomenlehre  der  Augen- 
muskettahmungen.  Berlin,  1867.  —  Donders  (F.  C.).  Anomalies  of  the  Refraction  and  Accommo- 
dation of  the  Eye.  London,  1864.  Hansen-Grut  (E. ).  Pathogeny  of  concomitant  squinting  (Bow- 
man lecture).  Transactions  of  the  Ophthalmolog-ical  Society  of  the  United  Kingdom^  Vol.  X, 
1890.  —  Javal  (E.).  Manuel  du  strabisme.  Paris,  Masson,  1896. 


CHAPTER   XXV. 
OPTIC   ILLUSIONS. 

139.  —  We  designate  by  the  above  name  cases  in  which  the  visual 
impressions  give  rise  to  a  false  judgment  on  the  nature  of  the  object. 
Illustrations,  paintings  and,  generally,  all  representations  of  an  object 
have  the  effect  of  producing  these  illusions;  and  all  optic  instruments 
act  in  a  like  manner.  In  the  former  part  of  the  book  I  have  mentioned 
several  times  illusions  of  a  more  special  character ;  I  shall  here  describe 
briefly  some  others,  the  explanation  of  which,  in  most  cases,  is  quite 
obscure. 

a.  A  first  series  of  illusions  is  based  on  the  fact  that  a  line  or  space 
seems  larger  when  it  is  divided  than  when  it  is  not.  This  is  the  reason 


Fig.  195. 

why  the  two  parts  ab  and  be  of  the  line  (fig.  195)  have  the  same  length, 
but  that  still  the  part  be  appears  longer,  because  it  has  divisions.    The 


Fig.  196. 

two  illustrations  of  figure  196  are  square,  but  the  illustration  a  seems 
wider  and  the  illustration  b  higher,  on  account  of  the  divisions.     For 

338 


OPTIC  ILLUSIONS 


339 


the  same  reason,  a  space  filled  with  furniture  appears  larger  than  when 
it  is  empty. 

b.  Very  small  angles  are  estimated  to  be  larger  than  they  are  in 
reality.  The  following  illusions  may  be  considered  as  examples  of  this 
rule.  The  lines  ab  and  cd  of  figure  197  are 
situated  in  the  prolongation  of  each  other, 
but  cd  seems  displaced  upwards.  The  illusion 
increases  if  we  move  the  figure  farther  away. 
We  may  conceive  that  if  we  judge  the  acute 
angle  to  be  too  large,  the  line  cd  ought  to 
seem  to  have  undergone  a  rotation  around  the 
point  c,  the  line  ab  around  the  point  b,  which 
would  produce  the  illusion  in  question. 

The  same  error  of  judgment  seems  to  take 
place  in  the  illusion  produced  by  the  designs 
of  figure  198  (Hering)  and  figure  199  (Zollner). 

In  figure  198  the  long  lines  are  straight  and  parallel,  but  seem  curved  ; 
in  the  upper  part  of  the  figure  they  appear  to  have  their  concave  sides 
turned  towards  each  other;  in  the  lower  part  the  contrary  takes  place. 


197. 


Fig.  198. 

In  the  figure  of  Zollner,  the  long  straight  lines,  which  are  parallel,  seem 
to  converge  or  diverge  upwards,  following  the  direction  of  the  small 
oblique  lines.  We  can  conceive  that  these  illusions  would  be  produced 
if  the  judgment  attributes  a  too  large  size  to  the  acute  angles.  Accord- 
ing to  Helmholtz,  the  movements  of  the  look  play  a  great  part  in  the 
production  of  these  illusions;  they  appear  much  more  pronounced  if 
we  keep  the  look  quiet.  If  we  bring  a  point  slowly  from  right  to  left 


340 


PHYSIOLOGIC  OPTICS 


in  front  of  the  figure  of  Zollner,  while  fixing  it  with  the  look,  the  lines 
seem  to  move;  those  which  appear  to  incline  their  upper  extremity  to 


1 

m 


K 


*  > 

J5 

;> 
Z 

s/ 

\i 


Fig.  199. 

the  right  seem  to  ascend,  while  the  others  seem  to  descend,  and  the  in- 
clination seems  at  the  same  time  more  pronounced.     If  we  bring  the 


/K 


\x 


Fig.  200. 


point  from  left  to  right,  the  lines  affect  a  reverse  movement.  The  ex- 
periment is  not  very  easy  to  perform,  but  we  can  obtain  the  same  effect 
more  easily  by  keeping  the  point  which  we  fix  motionless  and  moving 
the  drawing. 


OPTIC  ILLUSIONS  341 

c.  The  two  long  straight  lines  of  figure  200  have  the  same  length,  but 
b  appears  smaller  than  a. 

d.  We  frequently  estimate  cylinders  too  large.     If  we  place  a  large 
bottle  on  a  sheet  of  paper,  and  trace  its  circumference,  we  can  with 
difficulty  conceive,  after  having  taken  away  the  bottle,  that  we  are  not 
deceived,  so  small  is  the  circle.     Another  error  of  judgment  is  well 
known:  we  present  a  tall  hat  to  some  one,  asking  him  to  indicate  on 
the  wall  its  height,  starting  from  the  ground.     Generally  the  height 
pointed  out  is  about  half  too  large. 

e.  I  have  already  mentioned  the  reverse  of  relief  which  we  observe 
when  we  change  the  stereoscopic  images  sideways,  and  which  is  known 
under  the  name  of  pscudoscopia.    We  sometimes  observe  the  same  phe- 
nomenon under  other  circumstances.    If,  for  example,  we  fix  with  one 
eye  the  posterior  part  of  the  upper  border  of  a  lamp  chimney,  we  obtain 
quite  easily  the  illusion  that  this  part  is  in  front,  and  the  glass  seems 


Fig.  201. 

at  the  same  time  to  lean  towards  the  observer.  —  Observing  with  one 
eye  the  cast  of  a  medal,  it  may  be  difficult  to  tell  whether  the  figure  is 
hollow  or  in  relief. 

Analogous  phenomena  often  present  themselves  in  cases  in  which  a 
drawing  may  be  interpreted  in  two  different  ways.     Thus  figure  201 


342  PHYSIOLOGIC  OPTICS 

seems  composed  of  cubes,  the  illuminated  side  of  which  is  turned  some- 
times to  the  right,  sometimes  to  the  left.  When  one  interpretation  has 
predominated  for  a  certain  time,  the  other  suddenly  presents  itself.  We 
can  instigate  the  change  by  quickly  imagining  the  contrary  relief. 

f.  We  mention,  finally,  the  illusions  of  movements  of  exterior  ob- 
jects, which  often  present  themselves  in  consequence  of  the  false  judg- 
ment of  the  movements  which  we  ourselves  make.  One  of  the  best- 
known  examples  is  that  of  the  apparent  movements  of  objects  when 
we  are  traveling  by  rail;  the  traveler  does  not  take  into  account  his 
own  change  of  position  and  attributes  the  movement  to  the  exterior 
objects.  The  reverse  illusion  often  presents  itself  when  one  train  stops 
alongside  of  another ;  if  the  latter  is  put  in  motion,  we  often  attribute 
the  movement  to  our  own  train.  Waltzers  see  exterior  objects  rotate 
around  them  in  a  direction  contrary  to  their  own  rotation.  The  move- 
ment seems  to  continue  for  some  time  after  stopping,  on  account  of 
the  persistence  of  the  jerking  movements  of  the  eyes  (page  299). 

Generally,  exterior  objects  do  not  appear  to  be  displaced  during  the 
movements  of  the  look,  but  if  we  bring  the  look  quickly  from  one  of 
the  limits  of  the  field  to  the  other,  exterior  objects  seem  to  move  in 
the  contrary  direction. 

Aubert  has  described  the  following  illusion,  which  is  due  to  a  like 
reason.  In  the  shutter  of  a  completely  dark  room  we  make  a  vertical 
slit,  which  is  then  the  only  object  visible.  Leaning  the  head  towards 
one  of  the  shoulders,  the  slit  seems  to  undergo  a  rotation  in  the  reverse 
direction ;  it  no  longer  appears  vertical.  We  judge  the  inclination  of  the 
head  to  be  less  than  what  it  is,  almost  in  the  same  manner  as  the  move- 
ments which  we  cause  the  eyes  to  make  while  keeping  the  lids  closed, 
always  seem  less  than  they  really  are.  The  experiment  also  succeeds 
outside  of  the  dark  room,  especially  if  we  place  ourselves  in  such  a 
way  as  not  to  see  any  other  lines,  the  direction  of  which  we  know  to  be 
vertical. 

Bibliography.  —  Zollner.  Ueber  eine  neue  Art  von  Pseudoscopie.  Pogg.  Ann.,  CX,  p. 
500.  —  Hering  (E.).  Bdtrage  zur  Physiologic.  Leipzig,  1861,  I,  p.  65.  —Aubert  (H.). 
Physiologic  der  Netzhaut.  Breslau,  1865. 


TREATISES  TO   CONSULT. 


GEuvres  ophtalmologiques  of  THOMAS  YOUNG,  translated  and  annotated  by  M.  TSCHER- 
NING.  Copenhagen,  Hoest,  1894.  The  memoires  of  Young  were  published  at  the  beginning 
of  the  century  in  the  Transactions  of  the  Royal  Society  of  London  and  reprinted  in  his  Lec- 
tures (London,  1807).  A  later  reprint  in  Peacock  Works  of  Thomas  Young,  London,  1855,  is 
not  to  be  recommended,  the  reproduction  therein  of  the  pretty  illustrations  of  Young  being 
quite  defective.  The  works  of  Young  are  often  of  a  very  difficult  reading,  but  many  of  the 
modern  ideas  on  ocular  dioptrics  and  on  the  vision  of  colors  dated  from  him.  On  account  of 
the  great  importance  of  the  works  of  Young,  I  have  published  a  French  edition  of  them 
which  I  have  tried  to  make  of  an  easier  reading  by  explanatory  notes. 

v.  HELMHOLTZ  (H.).  Handbuch  der  physiologischen  Optik.  Leipzig,  1867.  This  monu- 
mental work  is  indispensable  to  all  those  who  desire  to  make  a  profound  study  of  physiologic 
optics,  but  it  is  not  a  very  easy  study.  The  book  contains  nearly  all  that  was  known  on  the 
subject  of  physiologic  optics  at  the  time  of  its  appearance  and  a  complete  bibliography.  In 
1885,  the  author  began  a  new  edition  of  it  (Leop.  Voss,  Hamburg),  which  was  continued 
after  his  death  by  A.  KCENIG.  The  only  difference  between  it  and  the  former  consists  of  a 
number  of  intercalations,  which,  however,  are  not  of  very  great  importance,  if  we  except 
those  of  the  second  part  which  contain  the  results  of  the  researches  on  the  vision  of  colors 
of  Kcenig,  Dieterici,  Brodhun,  Uhtho/,  etc.  The  latter  portion  of  the  work  contains,  from  the 
hand  of  K&nig,  a  complete  bibliography,  which  will  be  very  useful  to  the  investigators  of 
the  future. — The  work  of  HELMHOLTZ  was  translated  into  French  by  E.  JAVAL  and  N.  T. 
KLEIN  (Masson,  1867),  but  this  translated  edition  is  exhausted. — The  student  of  physiologic 
optics  must  not  dispense  with  reading  the  original  memoirs  of  this  great  scholar. 

HERMANN  (L.).  Handbuch  der  Physiologie  der  Sinnesorgane.  2vol.  Leipzig,  1879.  The 
part  which  has  to  do  with  vision  has  been  treated  by  FICK  (A.)  (Dioptrics),  KUEHNE 
(Chemistry  of  the  Retina]  and  HERINO  (E.)  (Movement  of  the  Eyes,  Binocular  Vision). 

Less  important  works  and  of  an  easier  reading  : 

FICK  (A.).    Lehrbuch  der  Anatomie  und  Physiologie  der  Sinnesorgane.    Lahr,  1864. 

KATSER(H.).  Compendium  der  physiologischen  Optik.  Wiesbaden,  1872.  Apart  from  some 
parts  which  the  author  has  treated  in  an  original  manner,  this  work  is  an  extract  from 
v.  HELMHOLTZ. 

AUBERT  (H.).  Physiologische  Optik,  in  Handbuch  der  gesammten  Augenheilkunde  von  A. 
ORAEFE  und  TH.  SAEMISCH.  Leipzig,  1876.  The  most  original  part  is  an  extract  from : 

AUBERT  (H.).  Physiologie  der  Netzhaut.  Breslau,  1865,  a  book  which  contains  a  great 
number  of  very  elaborate  researches  on  the  retinal  functions. 

LE  CONTE  (JOSEPH).  Sight.  London,  1881.  In  spite  of  some  errors  this  work  is  very 
instructive  on  account  of  its  originality. 

From  the  time  prior  to  v.  HELMHOLTZ  dates  MACKENZIE  ( W. ).  The  Physiology  of  Vision. 
London,  1841,  being  based  especially  on  the  works  of  YOUNO  and  WHEATSTONE. 

343 


844  PHYSIOLOGIC  OPTICS 

What  was  known  on  the  subject  of  physiologic  optics  in  the  last  century  is  found  in : 
PORTERFIELD  (WILLIAM).  A  Treatise  on  the  Eye.  2  vol.  Edinburgh,  1759,  and  in: 
JUBIN  (JACQUES).  Essai  sur  la  vision  distincte  et  indistincte  in  the  great  treatise  on  optics 

of  EGBERT  SMITH  ( A  Complet  System  of  Opticks).    London,  1738.    In  French  Cours  complet 

tfoptique  of  EGBERT  SMITH,  translated  by  PEZENAS.    Paris,  1767. 

The  work  of  JURIN  on  indistinct  vision  is  still  the  best  on  this  somewhat  neglected 
question. 

Of  the  works  on  more  or  less  important  branches  of  physiologic  optics  we  may  cite : 
BONDERS  (F.  C.).  On  the  Anomalies  of  Accommodation  and  Refraction  of  the  Eye.  London, 

1864.   In  German  by  O.  BECKER.   Wien,  1866.   In  French  by  E.  JAVAL,  in  DE  WECKER. 

Traite  des  maladies  des  yeux.    Paris,  1866.    On  account  of  its  remarkable  clearness  BONDERS 

is  of  a  very  easy  reading,  and  may  be  recommended  to  every  young  medical  student  who 

desires  to  begin  the  study  of  this  branch  of  ophthalmology. 

The  same  subject  has  been  treated  in : 

NAGEL  (A.).  Die  Anomalien  der  Refraction  und  Accommodation  des  Auges  in  Grafe  und 
Sdmisch.  Handbuch  der  Augenheilkunde.  Leipzig,  1880. 

LANDOI/T  (E.),  in  DE  WECKER  and  LANDOI/T.    Traite  complet  d'ophtalmologie,  1884. 

MAUTHNER  (L.).    Vorlesungen  iiber  die  optischen  Fehler  des  Auges.    Wien,  1876. 

MAUTHNER  (L.).  Farbenlehre.  Second  edition.  Wiesbaden,  1894.  The  books  of  Mauth- 
ner  are  written  in  a  very  clear  style  and  bear  the  impress  of  great  learning. 

Memoires  d'ophtalmometrie,  annotated  and  preceded  by  an  introduction  by  E.  JAVAI,. 
Paris,  Masson,  1890.  This  work  contains  a  great  number  of  notes  on  ophthalmometry  by 
different  authors. 

E.  JAVAL.  Manuel  de  Strabisme.  Paris,  Masson,  1896.  This  work  is  important  for  the 
study  of  binocular  vision. 


INDEX 


Abduction,  301 

Aberration,  chromatic,  80,   100,   109,  in, 
114 

produced  by  accommodation,  175 

spherical,  80,  95,  104 
Aberroscope,  the,  102 
Aberroscopic  phenomena,  144,  145,  171 
Absorption  of  light,  2 
Accommodation,  38 

amplitude  of,  81,  160 

astigmatic,  129 

author's  theory  of,  167 

central  and  peripheral,  173 

Cramer's  theory  of,  164 

Helmholtz  theory  of,  165 

H.  Muller's  theory  of,  166 

influence  of,  313 

mechanism  of,  162,  163,  165,  167 

paralysis  of,  161 

relative  amplitude  of,  303 

skiascopic  examination  of,  174 

spasm  of,  162 

Young's  theory  of,  167 
Accommodation  and  convergence,  relation 

between,  303 
Achloropsia,  268 
Acuity,  visual,  278 

peripheral,  282 
Adduction,  301 
Aerial  images,  34 

perspective,  314 
After-images,  241 

positive,  242 

negative,  242 
Akyanopsia,  268 
Amblyopia  exanopsia,  333 
Ametropia,  8 
Anaglyphs,  322 
Anerythropsia,  268 
Angle  alpha,  36,  63 

critical,  9 

meter,  302 

of  convergence,  10 

of  deviation,  10 

of  incidence,  2 

of  refraction,  2 

of  visibility,  279 
Aniridia,  165 
Antagonism  of  the  visual  fields,  323 


Aperture  of  an  optic  system,  34 

Aphakia,  80,  92 

Asthenopia,  accommodative,  91,  161 

of  astigmatic  patients,  132 

tarsal,  148 
Astigmatic  persons,  examination  of,  133 

surfaces,  62 
Astigmatism,  115,  137 

against  the  rule,  125 

by  incidence,  96,  119 

crystalline,  125 

corneal,  122,  123,  125,  128 

irregular  80,  137,  139 

latent,  129 

oblique,  125 

of  the  human  eye,  121 

physiologic,  122 

post-operative,  130 

produced  by  the  form  of  the  surfaces,  115 

regular,  80,  115,  118 

ophthalmometric  and  subjective,  125 

supplementary,  126 

symptoms  of,  132 

with  spherical  aberration,  140 

with  the  rule,  125,  132 
Arteries,  pulsation  of,  199 
Atropine,  212 
Auto  ophthalmoscope,  200 


Base  line,  302 

Binocular  ophthalmoscope,  321 

Binocular  vision,  287 

projection  in,  307 

theories  of,  325,  326,  328 
Black,  sensation  of,  238 

absolute,  238 
Brightness,  236 
Brushes  of  Haidinger,  157 


Cardinal  points,  19 

methods  of  finding,  20,  21 
of  the  crystalline  lens,  24 
of  the  human  eye,  32 

Cataract,  168,  233 

Cat's  eye,  amaurotic,  190,  191 

Centering,  defect  of,  66 


345 


Characteristic  part  of  a  pencil  of  light,  139 

Chess-board  of  Helmholtz,  216 

Chromatic  aberration,  80,  loo,  109,  in,  114 

correction  of,  1 14 

Chromatoptometer  of  Chibret,  270,  271 
Ciliary  corona,  157 
Ciliary  muscle,  discovery  of.  169 

structure  of,  170,  186,  187 
Cocaine,  212 
Color  blindness,  263 
Color-box  of  Maxwell,  248,  253 
Color  curves  of  Maxwell,  254 

of  a  dichromatic.  267 
Color  phenomena  of  contrast,  238,  241 
Colors,  complementary,  238 

equation  of,  247 

methods  of  mixing   247 

results  of  mixtures  of,  250 

sensations  of,  237 

spectral,  248 

the  principal,  272 

the  standard,  253 
Color  sense,  234 

clinical  examination  of,  269 
Color  table  of  Helmholtz,  260 

of  Maxwell,  252,  256,  265 

of  Newton,  237,  250 
Color  vision,  mechanism  of,  272 

Ebbinghaus's  theory,  275 

Helmholtz  theory,  273 

Hering's  theory,  274 

Koenig's  theory,  275 

Parinaud's  theory,  275 

Young's  theory,  272 
Concave  spherical  mirrors,  3 

aperture  of,  3 

apex  of,  3 

axis  of,  3 

principal  focus  of,  3 

principal  focal  distance  of,  3,  6 

reflection  on,  4 
Conjugate  points,  2,  5 
Conoid  of  Sturm,  115 
Contact  glasses,  145 
Contact  of  corneal  images,  48 
Controlled  reading,  336 
Convergence,  defect  of,  302 

measurement  of,  301 

negative,  300 
Convex  mirrors,  6 
Co-ordinates,  center  of,  306 

polar,  306 
Cornea,  basilar  part  of,  56 

conical,  54 

examination  of  peripheral  parts  of,  56 

increase  in  curvature  of,  162 

in  keratoconus,  59,  60,  6l 

optic  part  of,  56 

refracting  power  of,  31,  57 

results  of  measurements  of,  54 

utilized  part  of.  53 
Crystalline  lens,  28 

accommodative  layer  of,  184 

advance  of,  162 

astigmatic  accommodation  of,  128 


Crystalline  lens,  catoptric  images  of,  163,164 

change  in  thickness  of,  182 

contents  of,  184 

cortical  portion  of,  30 

deformity  of,  during  accommodation,  179 

increase  in  curvature  of,  162 

measuring  aberration  of.  107 

measuring  surfaces  of,  67,  68,  69,  70 

luxation  of,  80 

nucleus  of,  30,  184 

obliquity  of,  128 

refracting  power  of,  31 

total  index  of,  30 
Cylindrical  glasses,  121,  134 
Czermak,  experiment  of,  75 


Daltonism,  263 

bilateral,  264 

monolateral,  264 
Decentered  eyes,  131 

Deformity  of  internal  surfaces  in  astigma- 
tism, 126 

Descartes,  law  of,  8,  20 
Dichromasia,  263,  266 
Dichromatopsia,  263 
Diffraction  in  the  eye    157 
Diffusion  circles,  73   98,  172 

size  of,  73 

examination  of,  98 
Diplopia.  physiologic  binocular,  307 

paradoxical,  334 
Disc  keratoscopic,  61 

of  Benham,  230 

of  Helmholtz,  230 

of  Masson,  229 

of  Placido,  6 1 

ofVoIkmann,  295 
Dispersion,  109,  113 
Distance,  indirect  judgment  of,  313 

sensation  of,  332 

Doubling, methods  of  in  ophthalmometry,48 
Dove,  experiment  of,  240 


Empiric  theories,  217 
Entoptic  phenomena,  147 

analysis  of,  151 

manner  of  observing,  147 

parallax  of,  151 

Entoptic  object,   determination  of  position 
of,  152 

examination  of  refraction  of,  152 
Entoptic  observation  of  vessels  of  retina,  153 
Entoptoscope,  the,  150 
Eye,  an  artificial,  218 

aperture  of  the  optic  system  of  the,  34 

color  of  fundus  of  the,  198 

center  and  axes  of  rotation  of,  287 

directing,  308 

emmetropic,  8l 

methods  of  illuminating  fundus  of  the,  190 

muscles  of,  289 


340 


Eye,  optic  axis  of  the,  37 
optic  constants  of  the,  27 
optic  system  of  the,  27,  31 
schematic,  of  Helmholtz,  28 
the  simplified,  26 

Eyes,  associated  movements  of  the,  300 
jerking  movements  of  the,  299 
relative  movements  of  the  two,  299 
rotary  movements  of,  297 

Erect  image,  examination  by,  193,  197 

Eserine,  212 

Exophoria,  331 


Far  point,  8 1 
Fixation,  point  of,  36 
Fechner,  law  of,   224 

explanation  of  the,  224 

verification  of  the,  225,  226,  227 
Focal  distance,  anterior,  19 

of  a  convex  mirror,  6 

of  a  concave  mirror,  7 

posterior,  II,  19 

principal,  3 
Focal  interval  of  Sturm,  163 

lines,  115,  116,  143 
Focus,  anterior,  19 

posterior,  19 

principal,  3,  4 
Form  sense,  the  277 

measure  of  the,  277,  279 
Foucault,  principle  of,  99 
Fovea,  36,  79,  198,  221,  232 
Fraunhofer,  experiments  of,  112 

lines  of,  no,  235,  245 


Gauss,  theory  of,  18,  34 

Glabella,  310 

Globe,  elongation  of,  162,  168 


H 

Hemeralopia,  232 

Hess  and  Heine,  observations  of,  181,  188 

Homatropine,  212 

Hooke,  experiments  of,  277,  278 

Horopter,  310 

Hue,  of  color,  236 

changes  of,  236 
Hypermetropia,  80,  82,  90 

absolute,  90 

axial,  79 

correction  of,  82 

latent,  90,  194 
Hypoconchia,  86 


Iconoscope  of  Javal,  321 
Identical  points  of  the  retina,  324 
Identity,  theories  on  the  nature  of,  325 


Image,  2 

defects  of  the,  118 

erect,  examination  by,  193,  197 

inverted,  examination  by,  200 

of  mirrors,  3,  4 

of  lenses,  15 

of  any  optic  system,  20 

produced  by  a  small  aperture,  2 

real,  2 

useful,  37 

virtual,  2 
Images,  displacement  of  in  accommodation, 

180,  181. 

manner  of  observing  the,  42,  45 

of  Purkinje,  28,  29,  40,  42,  64,  65 

of  the  eye,  false,  39 

of  the  second  order,  false,  44 

suppression  of  double,  311 
Innervation,  judgment  of,  305 
Intensity,  236 

Inter-focal  distance,  115,  116 
Internal  surfaces,  position  of,  67 

centers  of,  69 

deformity  of,  126 

Interval  of  an  optic  system,  22,  25 
Inverted  image,  examination  by,  200 
Iris,  164 

apparent,  34 
Iridodonesis,  213 
Isopters,  283 


Jaeger,  test-types  of,  280 
Javal,  test  chart  of,  280 
Judgment,  unconscious,  313 


K 

Keratoconus,  80,  131,  176,  177 
Keratoscope  of  de  Wecker  and  Massilon,  1 76 
Keratoscopic  disc,  6l 
image,  60,  61,  62,  63 


Lens,  14 

achromatic,  ill 

aplanatic,  95 

axis  of,  14 

concave,  16 

crossed,  96 

crown,  96 

flint,  96 

focal  distance  of  a,  14,  17 

infinitely  thin,  14,  23 

measuring  focal  distance  of,  17 

optic  center  of,  14 

over-corrected,  95 

phenomena  dependent  on  spherical  ab- 
erration of,  96 

refracting  power  of,  18 
Lenticonus,  80 

false,  80 


34: 


Leucotna,  central,  233 
Leucoscope,  the,  270 
Light,  harmful,  39 

lost,  39 

monochromatic,  157,  234 

quantity  reflected,  8 

rectilinear  propagation  of,  I 

useful,  39 
Light  sense,  the,  224 

measurement  of,  228 
Lithium  flame,  234 
Listing,  axes  of,  293 

law  of,  217,  218,  289,  290,  292,  294,  296, 

297 
Luminous  point,  analysis  of  the,  143 

figures  of,  143 
Luminous  rays,  I 

incident,  3 

reflected,  3 


M 

Macula,  198,  233,  262 

Maddox  test,  331 

Meissner,  experiments  of,  294 

Menisci,  16 

Meridian,  apparently  vertical,  294 

Meter  angle,  302 

Meyer,  H.,  experiment  of,  239 

Micrometer,  197 

Microphthalmia,  55 

Mile,  experiment  of,  75 

Mires,  47 

Mirrors,  concave  spherical,  3 

plane,  3 

portion  of  used,  7 
Monochromasia,  269 
Musca-  volitantes,  149,  155 
Mydriatics  and  myotics,  212 
Myopia,  80,  84,  89,  163 

atropine  treatment  of,  89 

axial,  79 

correction  of,  81 

dangerous,  84 

treatment  of,  89 


N 

Nativistic  theories,  219 
Near  point,  8 1 

determination  of,  160 
Neutral  point  in  the  spectrum  of  color-blind, 

263 

Nicol  prism,  157 
Nodal  points,  19,  32 
Normal,  of  a  surface,  14 
Nyctalopia,  233 


Oblique  illumination,  213 
Ocular  movements,  287,  299 
muscles,  action  of,  289 


Opaque  bodies,  I 
Ophthalmometer,  48,  49,  50 

of  Brudzewski,  59 

of  Helmholtz,  49,  56 

of  Javal  and  Schioetz,  51,  56 
Ophthalmometry,  47 

Ophthalmodynamometer  of  Landolt,  302 
Ophthalmophakometer,  44,  64,  175,  179 
Ophthalmoscope,  190 

binocular,  321 

of  Coccius,  7 

of  Cramer,  163,  189 

of  Helmholtz,  192 

principle  of,  192 

Ophthalmoscopic  examination  of  refracting 
media,  204 

field,  196,  202 

magnification,  by  erect  image,  194 

magnification  by  inverted  image,  200 
Ophthalmoscopy,  190 
Optic  axis,  36 

constants  of  the  eye,  27 

illusions,  338 

properties  of  bodies,  I 
Optic  system  of  the  cornea,  31 

of  the  crystalline  lens,  31 

of  the  eye,  31 

aperture  of  the  eye,  34 

obliquity  of  the  eye,  143 
Optogram,  221 
Optometer,  83 

of  Badal,  160 

of  George  Bull,  160 

of  Mile,  75 

ofScheiner,  75 

ofWeiland,  135 

of  Young,  75,  144,  173 


Papillary  excavations,  197,  199 
Papilla,  197,  198,  238 

scleral  border  of,  199 
Paracentesis,  189 
Paracentral  shadow,  209 

theory  of,  209 

explanation  of,  209 

Parallax,  influence  of  the  binocular,  317 
Penumbra,  2 
Perception  of  depth,  monocular,  313 

binocular,  317 
Periscopic  glasses,  96,  135 
Phosphene  of  Czermak,  156 
Phosphorescence,  190 
Photoptometer  of  Charpentier,  228,  247 

of  Foerster,  228 
Placido,  disc  of,  61 
Plates  of  Helmholtz,  204 
Point  of  fixation,  36 
Position  of  anatomic  equilibrium,  334 

of  cardinal  points,  25 

of  the  centers,  67 

of  the  surfaces,  67 

of  functional  equilibrium  of  eye,  334 


348 


Presbyopia,  161 

Primary  direction  of  eye,  289 

position,  289 
Principal  focus,  3,  4 

focal  distance,  3 

meridians,  115 

planes,  19 

points,  19 
Prism,  achromatic,  no,  in 

a  vision  directt,  no,  in 

Nicol,  157 

refraction  by  a,  IO 

with  total  reflection,  9 

Wollaston,  50 

Projection  in  binocular  vision,  307 
Projections,  center  of,  307 

general  laws  of,  304 

theory  of,  325 
Pseudoscope,  the,  320 
Pseudoscopia,  341 
Punctura  proximum,  76,  8 1 

remotum,  76,  8l 
Pupil,  211 

apparent,  34,  21 1 

contraction  and  dilatation  of,  21 1 

in  accommodation,  213 

influence  of  light  on,  212 

movements  of,  212 

nerve  control  of,  21 1 

of  albinos,  191 

of  entrance,  35 

of  exit,  35 

real,  34 

variations  of  refraction  in,  145 
Purity  of  color,  236 


Radii,  direct  determination  of,  70 
Radius  vector,  306 
Ragona  Scina,  experiment  of,  239 
Reflection,  2 

images  of  the  eye,  176,  177 

regular,  2 

total,  8 

on  a  concave  mirror,  4 

on  a  plane  mirror,  3 
Refracting  surface,  power  of,  13 

simple,  23 
Refraction,  8 

anomalies  of,  79 

by  a  parabolic  surface,  178 

by  a  prism,  lo 

by  a  spherical  surface,  II,  12 

by  plane  parallel  plates,  10 

by  a  surface  of  revolution  of  the  second 
degree,  13 

index  of,  8 

in  the  pupil,  145 

ophthalmoscopic  and  subjective,  197 
Relief,  idea  of,  327 

measurement  of,  327 

theory  of,  326 
Retina,  219,  221 


Retina,  changes  of,  221 

detachment  of,  232 

functions  of,  221 

pigment  of,  222 
Retina  of  frog,  section  of,  223 
Retina  seen  by  the  ophthalmometer,  199 
Retina's  own  light,  226 
Retinal  horizon,  294 
Retinal  purple,  198,  221 

discovery  of,  222 
Retinal  oscillations,  243 


Saturation  of  color,  236 

Scheiner,  experiment  of,  75,  96,  249 

Scopolamine,  212 

Secondary  direction,  289 

Shade  of  color,  236 

Shadows,  I 

colored,  239 

deformity  of  the,  98 

experiments  with,  240 
Sight,  line  of,  74 

Skiascopic  examination  for  astigmatism,  134 
206 

field,  20 

examination  of  optic  anomalies,  210 
Skiascopy,  205 

application  of,  205 

with  concave  mirror,  205 

with  plane  mirror,  205 
Snellen,  charts  of,  279 
Sodium  flame,  234 
Spectacles,  choice  of,  87,  161 
Spectroscope,  234 
Spectrum,  234 

colors  of,  236 

of  diffraction,  235 

of  refraction,  236 
Spot  of  Mariotte,  63,  238,  284 
Spherical  aberration,  80,  95,  104 
Spherometer,  17 
Staphyloma,  197 
Stenopaic  opening,  77 
Stereoscope,  317 

effect  of,  322 

of  Helmholtz,  320 

of  Wheatstone,  320 
Stereoscopic  exercises,  336 

images,  methods  of  observing,  319 

lustre,  322 

parallax,  318 

photographs,  322 
Strabismic  patients,  vision  of,  334 
Strabismus,  329 

cause  of,  333 

concomitant,  329,  330,  332 

convergent,  of  myopes,  334 

latent,  330 

measurement  of,  331 

nature  of,  333 

paralytic,  329 

relation  between  convergent  and  hyper- 
metropia,  332 


349 


Strabismus,  relation  between  divergent  and 

myopia,  333 
treatment  of,  335 
Strontium  flame,  237 
Synchisis  scintillans,  204 
Syringe  of  Pravaz,  189,  214 


Tapetum,  190 
Telescopic  system,  22 
Telestereoscope  of  Helmholtz,  321 
Thallium  flame,  234 
Threshold,  the,  227 

determination  of  231 
Tint,  236 
Tore,  119,  136 
Translucent  bodies,  I 
Transparent  bodies,  I 
Trichromasia,  abnormal,  261 
Triplopia,  binocular,  335 
Troxler,  phenomenon  of,  242,  285 


Veins,  pulsation  of,  199 
Vision,  "recurrent,"  243 

single,  antipathy  to,  336 
Visual  acuity,  278 

central,  277 

measurement  of,  278,  279 

peripheral,  282 
Visual  acuity  and  illumination,  relation  b&. 

tween,  281 

Visual  field,  projection  of  the,  304 
Visual  fields,  antagonism  of  the,  312,  323, 
Visual  impressions,  projection  of,  304 
Visual  line,  36 
Volkmann,  disc  of,  295 

experiments  of,  loo 


W 

White,  normal,  of  Koenig   238 
Wollaston,  experiment  of,  ill 
prism  of,  50 


LIST  OF  AUTHORS 


Abbe,  26,  28.  35. 

Agabobon,  243. 

Airy,  121. 

Almeida  (d'),  322. 

Argyll  Robertson,  213. 

Arlt,  86,  94,  163,  171,  187,  213,  214,  220. 

Aubert,  56,  72,  261,  342,  343. 

Babbage,  193. 

Badal,  83,  84,  160,  202. 

Becker,  46,  344. 

Beer,  190. 

Bellarminoff,   191,  210. 

Benham,  230 

v.  Bezold,  114. 

Bidwell,  243. 

Bitzos,  209,  210. 

Bjerrum,  202,  210,  231,  233,  283,  286. 

Blix,  46. 

Boehm,  91,  94,  332,  337. 

Boll,   222,   223. 

Bouguer,  225,  228,  233. 

Bourgeois,  55. 

Bouty,  26. 

Bowman,  169,  189. 

Brewster,  151,  152,  159,  319,  328. 

Brodhun,  244,  276. 

Brown-Sequard,  211. 

Brudzewski,  59,  72,  105,  106,   108. 

Bruecke,  no,  169,  189,  190,  193,  210,  326, 

328. 
Bull  (George),  129,  133,  136,  148,  149,  160, 

161,  220. 
Burkhardt,  280. 
Burow,  153. 

Charpentier,  228,  233,  243,  247. 
Chibret,  270,  271,  276. 
Coccius,  46,  50,  83,  166,  187,  189,  210. 
Cohn,  86,  213,  270. 


Coronat,  164. 

Cramer,  163,  164,  165,  179,  181,  182,  186, 

189. 

Cretes,  301,  302,  332. 
Crzellitzer,  159,  186,  189. 
Cuignet,  205,  210. 
Gumming,  190,  193,  2 to. 
Czermak,  75,  156,  166. 

Daae,  270. 

Dalton,  263,  268,  276. 

Darier,  149,  159. 

Darwin,  219. 

Davis,  243. 

Demicberi,  30,  43,  80,  94,  145,  178,  184, 
204,  210. 

Descartes,  8,  20,  163 

Dieterici,  236,  259,  263,  266,  267,  276. 

Dimmer,  93,  94. 

Dobrowolsky,  129. 

Dojer,  287. 

Dollond,  in. 

Doncan,  151,  152,  159. 

Donders,  50,  54,  83,  86,  88,  89,  90,  91,  92, 
94,  121,  125,  136,  151,  152,  158,  161, 
169,  197,  219,  263,  264,  287,  289,  292, 

297.  298,  3°3,  332,  337.  344- 
Dove,  240,  322,  323. 
Druault,  157,  158,  159,  281. 
Dubois  (Raphael),  49 
Dubois-Reymond,  213,  220,  223. 

Ebbinghaus,  275,  276. 
Eissen,  125. 

Erikstn,  56,  57,  58,  59,  72,  120. 
Euler,  ill. 

Fechner,  224,  225,  226,  227,  228,  230,  231, 

232,  233,  243.  244. 
Fick,  294,  298,  343. 


Foerster,  170,  189,  228,  233. 
Fontana,  170. 

Fraunhofer,  no,  1 12,  114,  235,  245. 
Fukala,  89. 

Galien,  325. 

Gariel,  26. 

Gauss,  18,  19,  26,  27,  34. 

v.  Genderen  Stort,  222,  223. 

Giraud-Teulon,  321,  322,  325. 

Goulier,  12 1,  136. 

v.  Graefe,  83,  107,  189,  200,  329,  333,  334, 

336,  337- 

Graefe  (Alfred),  165,  189,  333,  337. 
Green,  280. 
Groenouw,  283,  286. 
Guillery,  281,  284,  286. 

Haidinger,  157,  159. 

Hamer,  54- 

Hansen  Grut,  232,  329,  331,  332,  333,  334, 

337- 

Hay,  292. 

Heath,  26. 

Heine,  181,  188,  189. 

v.  Helmholtz,  5,  26.  28,  30,  47,  49,  50,  54, 
56,  79,  109,  112,  114,  121,  149,  165, 
166,  167,  169,  170,  171,  181,  182,  183, 
184,  187,  188,  189,  190,  192,  193,  196, 
204,  210,  213,  216,  217,  218,  219,  230, 
248,  249,  251,  260,  268,  273,  274,  275, 
276,  277,  278,  279,  287,  290,  293,  298, 
314,  320,  321,  324,  328,  339,  343. 

Hencke,  166. 

Henle,  36. 

Hensen,  166,  187. 

Hering,  219,  269,  274,  275,  276,  291,  297, 
300,  309,  312,  339,  342,  343- 

Hermann,  128,  292,  343. 

Herschel,  26. 

Hess,  181,  188,  189. 

Ileuse,  46. 

v.  Hippel,  264,  265,  273. 

Hirschberg,  83,  332. 

Hocquard,  185. 

Holmgren,  268,  269. 

Holth,  60,  61,  184,  284,  285,  286. 

Home,  163. 

Hooke,  277,  278,  286. 

Hueck,  165,  181,  189,  213,  297,  298. 

Huyghens,  276. 


Iwanoff,  187. 

Jackson,  104,  108,  174,  210. 

Jaeger,  200,  280. 

Jamin,  26. 

Javal,  36,  40,  50,  51,  52,  55,  56,  60,  62,  72, 
83,  89,  114,  122,  123,  125,  126,  128,  131, 
132,  135,  138,  186,  231,  240,  280,  281, 
290,  296,  298,  302,  303,  308,  312,  321, 
323,  326,  327,  328,  331,  333,  334,  335, 

336,  337,  343.  344- 
Johnsson,  76. 
Jurin,  78,  344. 

Kagenaar,  50. 

Kaiser,  308,  312,  343. 

Kepler,  38,  163,  325. 

Klein,  233,  343. 

Knapp  (H.)t  I2I»  I25,  136. 

Knapp,  Jr.,  309. 

Kcenig,  236,  238,  244,  249,  259,  263,  266, 

267,  268,  270,  275,  276. 
Koster,  172,  176,  182,  275,  276. 
Krause,  183,  189. 
Krenchel,  232,  233,  270,  276. 
v.  Kries,  275,  276. 
Kuehne,  222,  223,  343. 

Laiblin,  156. 

Lambert,  225,  233,  238,  249,  276. 

Lamare,  299,  303. 

Landolt,  94,  297,  302,  332,  344. 

Langenbeck,  163,  189. 

Leber,  268. 

Le  Conte,  343. 

Leonardo  da  Vinci,  37. 

Leroy,  197,  208,  209,  210. 

Listing,  30,  38,  151,  159,  217,  218,  289,  290, 

292,  293,  294,  296,  297,  298,  311. 
Lorenz,  26. 

Mace  de  Lepinay,  244,  276. 

Mackenzie,  343. 

Maddox,  331. 

Mannhardt,  170,  189. 

Mariotte,  238,  283,  284,  285,  294. 

Martin,  125,  129. 

Mascart,  79,  no. 

Masselon,  123,  176,  177. 

Masson,  229,  230,  231,  233,  241,  249,  260. 

Matthiessen,  28,  30,  38,  56. 


352 


Mauthner,  50,  94,  166,  269,  344. 
Maxwell,  248,  249,  251,  252,  253,  254,  256, 

257,  258,  259,  260,  261,  262,  266,  267, 

273,  276. 

Meissner,  294,  296,  298. 
Meyer  (H.),  108,  239. 
Mile,  75,  78. 
Miiller  (H.),  153,  !54.  *59,  I66,  l69,  17°, 

189,  221,  275. 
Muller  (Joannes),  311,  312,  324,  325,  328. 

Nagel,  302,  303,  328,  344. 

Newton,  5,  81,  in,  237,  238,  250,  251,  252, 

255,  259,  276,  325,  328. 
Nicati,  244,  276. 
Nordenson,  125,  136. 

Ostwalt,  93,  94,  128. 

Panum,  326,  328. 

Parent,  205,  208,  210. 

Parinaud,  232,  245,  246,  247,  275,  276,333. 

Petit  (Jean  Louis),  183,  189. 

Pfalz,  125. 

Pfluger,  93,  239,  270. 

Placido,  61,  123. 

Porta,  37. 

Porterfield,  325,  344, 

Pouillet- Muller,  26. 

Pravaz,  189,  214. 

Preyer,  268. 

Prentice,  303,  332. 

Purkinje,  40,  41,  42,  44,  46,  64,  80,  153, 

I56»  *59i  l63,  l66i  *89,  200,  213,  242, 

243,  260,  276. 

Raehlmann,  333. 

Ragona  Scina,  239. 

Ramsden,  163. 

Rayleigh,  258,  262,  263,  276,  314. 

Ree,  139,  140,  141,  142,  143,  146. 

Risley,  87. 

Rochon  Duvignaud,  189. 

Rose,  270. 

Ruete,  200,  210,  297,  298. 

Salomonsohn,  157,  159. 
Scheiner,  38,  75,  76,  78,  96,  100,  162,  249. 
Scbioetz,  40,  50,  51,  52,  56,  123,  125,  136, 
138,  »57,  158,  159,  '86,  290,  332. 


Schlemm,  169. 

Schmidt- Rimpler,  204. 

Schweigger,  136,  333. 

Seebeck,  268,  270,  276. 

Smith  (Robert),  286,  344. 

Snellen,  84,  279,  280,  281. 

Snellius,  8. 

Sous,  83. 

Stadfeldt,  33,   38,  93,    106,   107,  108,  168, 

1 86,  189,  214. 
Steiger,  55. 

Stellwag,  91,  94,  281,  286,  333. 
Stilling,  86,  270. 
Stokes,  135. 

Sturm,  115,  132,  136,   163. 
Sulzer,  55,  56,  57,  58,  59,  72,  128,  129,  146. 

Troxler,  242,  285,  299. 
Tscherning,  38,  46,  50,  72,  78,  94,  108,  114, 
136,    146,  159,  189,  220,  276,  286,  298. 
Turk,  199. 

Uhthoff,  276. 

Vacher,  129. 
Verdet,  26. 
Vierordt,  156. 
Vcelkers,  166,  187. 

Volkmann,  100,  101,  108,  288,  295,  296, 
297,  298,  325,  328. 

Wecker  (de),  88,  123,  176,  204,  331,  333. 

Werlein,  75. 

Weyde  (v.  d.),  266. 

Wheatstone,  317,  319,  320,  326,  328,  336, 

343- 

Wollaston,  50,  ill,  114,  135,  325. 
Wullner,  26. 

Young,  30,  38,  47,  75,  77,  101,  102,  103, 
in,  112,  113,  121,  138,  144,  145,  156, 
157,  160,  161,  167,  168,  169,  173,  174, 
197,  220,  240,  255,  272,  273,  275,  298, 
3^3,  315,  3^6,  343- 

Zeiss,   ill. 

Zinn,  185. 

Zoellner,  339,  340,  342. 

Zumft,  275,  276. 


353 


THE 

PRINCIPLES  OF  REFRACTION 

in  the  Human  Eye,  Based  on  the  Laws  of 
Conjugate  Foci 

BY  SWAN   M.  BURNETT,  M.  D.,  PH.  D. 

Professor  of  Ophthalmology  and  Otology  in  the  Georgetown  University  Medical  School 
Director  of  the  Eye  and   Ear  Clinic,  Central   Dispensary  and  Emergency 
Hospital  ;  Ophthalmologist  to  the  Children's  Hospital  and  to 
Providence  Hospital,  etc.,  Washington,  D.  C. 


In  this  treatise  the  student  is  given  a  condensed  but  thor- 
ough grounding  in  the  principles  of  refraction  according  to  a 
method  which  is  both  easy  and  fundamental.  The  few  laws 
governing  the  conjugate  foci  lie  at  the  basis  of  whatever  pertains 
to  the  relations  of  the  object  and  its  image. 

To  bring  all  the  phenomena  manifest  in  the  refraction  of  the 
human  eye  consecutively  under  a  common  explanation  by  these 
simple  laws  is,  we  believe,  here  undertaken  for  the  first  time. 
The  comprehension  of  much  which  has  hitherto  seemed  difficult 
to  the  average  student  has  thus  been  rendered  much  easier.  This 
is  especially  true  of  the  theory  of  Skiascopy,  which  is  here  eluci- 
dated in  a  manner  much  more  simple  and  direct  than  by  any 
method  hitherto  offered. 

The  authorship  is  sufficient  assurance  of  the  thoroughness 
of  the  work.  Dr.  Burnett  is  recognized  as  one  of  the  greatest 
authorities  on  eye  refraction,  and  this  treatise  may  be  described 
as  the  crystallization  of  his  life-work  in  this  field. 

The  text  is  elucidated  by  24  original  diagrams,  which  were 
executed  by  Chas.  F.  Prentice,  M.  E. ,  whose  pre-eminence  in 
mathematical  optics  is  recognized  by  all  ophthalmologists. 

Bound  in  Silk  Cloth. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price, 
$I.OO   (4s.  2d.) 


published  by  THE  KEYSTONE, 

THE  ORGAN  OF  THE  JEWELRY  AND  OPTICAL,  TRADES, 

I9TH  AND  BROWN  STS.,  PHILADELPHIA,  U.S.A. 


THE  OPTICIAN'S  MANUAL 

VOL.  I. 

BY  C.  H.  BROWN,  M.  D. 

Graduate  University  of  Pennsylvania ;   Professor  of  Optics  and  Refraction  ;  formerly 

Physician  in  Philadelphia  Hospital ;  Member  of  Philadelphia  County, 

Pennsylvania  State  and  American  Medical  Societies. 


The  Optician's  Manual,  Vol.  I.,  has 
proved  to  be  the  most  popular  work  on 
practical  refraction  ever  published.  The 
knowledge  it  contains  has  been  more 
effective  in  building  up  the  optical  profes- 
sion than  any  other  educational  factor. 
A  study  of  it  is  essential  to  an  intelligent 
appreciation  of  Vol.  II.,  for  it  lays  the 
foundation  structure  of  all  optical  knowl- 
edge, as  the  titles  of  its  ten  chapters  show  : 


Chapter       I.— Introductory  Remarks. 

Chapter  II.— The  Eye  Anatomically. 

Chapter  III.— The  Eye  Optically ;  or,  The  Physiology  of  Vision. 

Chapter  IV.— Optics. 

Chapter  V. — Lenses. 

Chapter  VI. — Numbering  of  Lenses. 

Chapter  VII.— The  Use  and  Value  of  Glasses. 

Chapter  VIII.— Outfit  Required. 

Chapter  IX.— Method  of  Examination. 

Chapter  X.— Presbyopia. 

The  Optician's  Manual,  Vol.  I.,  is  complete  in  itself,  and 
has  been  the  entire  optical  education  of  many  successful  opti- 
cians. For  student  and  teacher  it  is  the  best  treatise  of  its  kind, 
being  simple  in  style,  accurate  in  statement  and  comprehensive 
in  its  treatment  of  refractive  procedure  and  problems.  It  merits 
the  place  of  honor  beside  Vol.  II.  in  every  optical  library. 

Bound  in  Cloth— 422  pages— colored  plates  and  Illustrations. 
Sent  postpaid  on  receipt  of  $1.5O   (6s.  3d.) 


published  by  THE  KEYSTONE, 

THE  ORGAN  OP  THE  JEWELRY  AND  OPTICAL.  TRADES, 

I9TH  &  BROWN  Sxs.,  PHILADELPHIA,  U.  S.  A. 


THE  OPTICIAN'S  MANUAL 

VOL.  II. 

BY  C.  H.  BROWN,  M.  D. 

Graduate  University  of  Pennsylvania ;  Professor  of  Optics  and  Refraction  ;    formerly 

Physician  in  Philadelphia  Hospital ;  Member  of  Philadelphia  County, 

Pennsylvania  State  and  American  Medical  Societies. 


TICIANS 


The  Optician's  Manual,  Vol.  II.,  is 
a  direct  continuation  of  The  Optician'  a 
Manual,  Vol.  I.  ,  being  a  much  more 
advanced  and  comprehensive  treatise. 
It  covers  in  minutest  detail  the  four 
great  subdivisions  of  practical  eye  refrac- 
tion, viz  : 


Myopia. 
Hypermetropia. 
Astigmatism. 
Muscular  Anomalies. 


It  contains  the  most  authoritative  and  complete  researches 
up  to  date  on  these  subjects,  treated  by  the  master  hand  of 
an  eminent  oculist  and  optical  teacher.  It  is  thoroughly  prac- 
tical, explicit  in  statement  and  accurate  as  to  fact.  All  refrac- 
tive errors  and  complications  are  clearly  explained,  and  the 
methods  of  correction  thoroughly  elucidated. 

This  book  fills  the  last  great  want  in  higher  refractive 
optics,  and  the  knowledge  contained  in  it  marks  the  standard 
of  professionalism. 

Bound  in  Cloth— 408  pages— with  illustrations. 
Sent  postpaid  on  receipt  of   SI.5O   (6s.  3d.) 


published  by  THE  KEYSTONE, 

THE  ORGAN  OF  THE  JEWELRY  AND   OPTICAL.  TRADES, 

I9TH  &  BROWN  STS.,  PHILADELPHIA,  U.  S.  A. 


OPHTHALMIC  LENSES 

Dioptric  Formulae  for  Combined  Cylindrical  Lenses, 

The  Prism-Dioptry  and  Other  Original  Papers 

BY  CHARLES  F.  PRENTICE,  M.  E. 


A  new  and  revised  edition  of  all  the  original  papers  of  this  noted 
author,  combined  in  one  volume.  In  this  revised  form,  with  the  addition 
of  recent  research,  these  standard  papers  are  of  increased  value.  Com- 
bined for  the  first  time  in  one  volume,  they  are  the  greatest  compilation 
on  the  subject  of  lenses  extant. 

This  book  of  over  200  pages  contains  the  following  papers  : 

Ophthalmic  Lenses. 

Dioptric  Formulas  for  Combined  Cylindrical  Lenses. 

The  Prism=Dioptry. 

A  Metric  System  of  Numbering  and  Measuring  Prisms. 

The  Relation  of  the  Prism-Dioptry  to  the  Meter  Angle. 

The  Relation  of  the  Prism-Dioptry  to  the  Lens  Dioptry. 
The  Perfected  Prismometer. 
The  Prismometric  Scale. 

On  the  Practical  Execution  of  Ophthalmic  Prescriptions  involving  Prisms. 
A  Problem  in  Cemented  Bifocal  Lenses,  Solved  by  the  Prism=Dioptry. 
Why  Strong  Contra=(ieneric  Lenses  of  Equal  Power  Fail  to  Neutralize 

Each  Other. 

The  Advantages  of  the  Sphero=Toric  Lens. 
The  Iris,  as  Diaphragm  and  Photostat. 
The  Typoscope. 
The  Correction  of  Depleted  Dynamic  Refraction  (Presbyopia). 

Press  Notices  on  the  Original  Edition : 

OPHTHALMIC  LENSES. 


"  The  work  stands  alone,  in  its  present 
form,  a  compendium  of  the  various  laws  of 
physics  relative  to  this  subject  that  are  so 
difficult  of  access  in  scattered  treatises." — 
New  England  Medical  Gazette. 

"  It  is  the  most  complete  and  best  illus- 
trated book  on  this  special  subject  ever  pub- 
lished."— Horological  Review \  New  York. 


"  Of  all  the  simple  treatises  on  the  prop- 
erties of  lenses  that  we  have  seen,  this  is  in- 
comparably the  best.  .  .  .  The  teacher  of 
the  average  medical  student  will  hail  this 
little  work  as  a  great  boon  " — Archives  oj 
Ophthalmology,  edited  byH.Knapp,  M.D. 


DIOPTRIC  FORMULA  FOR  COMBINED  CYLINDRICAL  LENSES. 


*'  This  little  brochure  solves  the  problem 
of  combined  cylinders  in  all  its  aspects,  and 
in  a  manner  simple  enough  for  the  compre- 
hension of  the  average  student  of  ophthal- 
mology. The  author  is  to  be  congratulated 
upon  the  success  that  has  crowned  his  labors, 
for  nowhere  is  there  to  be  found  so  simple 
and  yet  so  complete  an  explanation  as  is  con- 
tained in  these  pages." — Archives  of  Oph- 
thalmology, edited  by  H.  Knapp,  M.D. 


"This  exhaustive  work  of  Mr.  Prentice 
is  a  solution  of  one  of  the  most  difficult  prob- 
lems in  ophthalmological  optics.  Thanks 
are  due  to  Mr.  Prentice  for  the  excellent 
manner  in  which  he  has  elucidated  a  sub- 
ject which  has  not  hitherto  been  satisfactor- 
ily explained."—  The  Ophthalmic  Review, 
London. 


The  book  contains  HO  Original  Diagrams.    Bound  in  cloth. 
Price,  $I.5O  (6s.  3d.) 


published  by  THE  KEYSTONE, 

THE  ORGAN  OF  THE  JEWELRY  AND  OPTICAL  TRADES, 

I9TH  &  BROWN  STS.,  PHILADELPHIA,  U.  S.  A. 


SKIASCOPY 

AND  THE  USE  OF  THE  RETINOSCOPE 


A  Treatise  on  the  Shadow  Test  in 
its  Practical  Application  to  the 
Work  of  Refraction,  with  an  Ex- 
planation in  Detail  of  the  Optical 
Principles  on  which  the  Science 
is  Based. 


This  new  work,  the  sale  of  which  has  already  necessitated 
a  second  edition,  far  excels  all  previous  treatises  on  the  subject 
in  comprehensiveness  and  practical  value  to  the  refractionist. 
It  not  only  explains  the  test,  but  expounds  fully  and  explicitly 
the  principles  underlying  it — not  only  the  phenomena  revealed 
by  the  test,  but  the  why  and  wherefore  of  such  phenomena. 

It  contains  a  full  description  of  skiascopic  apparatus, 
including  the  latest  and  most  approved  instruments. 

In  depth  of  research,  wealth  of  illustration  and  scientific 
completeness  this  work  is  unique. 

Bound  in  cloth;   contains  231  pages  and  73  illustrations 
and  colored  plates. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  $I.OO   (4s.  2d.) 


published  by  THE  KEYSTONE, 

THE    ORGAN    OF    THE   JEWELRY    AND    OPTICAL    TRADES, 

IQTH  AND  BROWN  STS.,  PHILADELPHIA,  U.S.A. 


OPTOMETRIC  RECORD  BOOK 


A  record  book,  wherein  to  record  optometric  examinations, 
is  an  indispensable  adjunct  of  an  optician's  outfit. 

The  Keystone  Optometric  Record  Book  was  specially  pre- 
pared for  this  purpose.  It  excels  all  others  in  being  not  only  a 
record  book,  but  an  invaluable  guide  in  examination. 

The  book  contains  two  hundred  record  forms  with  printed 
headings,  suggesting,  in  the  proper  order,  the  course  of  examina- 
tion that  should  be  pursued  to  obtain  most  accurate  results. 

Each  book  has  an  index,  which  enables  the  optician  to  refer 
instantly  to  the  case  of  any  particular  patient. 

The  Keystone  Record  Book  diminishes  the  time  and  labor 
required  for  examinations,  obviates  possible  oversights  from 
carelessness  and  assures  a  systematic  and  thorough  examination 
of  the  eye,  as  well  as  furnishes  a  permanent  record  of  all  exam- 
inations. 

Sent  postpaid  on  receipt  of  $1  .OO  (4s.  2d.) 


published  by  THE  KEYSTONE, 

THE;  ORGAN  OF  THE;  JEWELRY  AND  OPTICAL  TRADES, 
i9TH  &  BROWN  STS.,  PHILADELPHIA,  U.S.A. 


ttfafofrel 


THE  LIBRARY 
UNIVERSITY  OF  CALIFORNIA 

San  Francisco  Medical  Center 
THIS  BOOK  IS  DUE  ON  THE  LAST  DATE  STAMPED  BELOW 

Books  not  returned  on  time  are  subject  to  fines  according  to  the  Library 
Lending  Code. 

Books  not  in  demand  may  be  renewed  if  application  is  made  before 
expiration  of  loan  period. 


30m-10,'61  (C3941s4)4128 


